Chaos rules at Baptista’s house the next morning as Katherine chases Bianca, cursing at her in a fury. Katherine has tied Bianca’s hands together and is trying to beat her sister because Bianca will not tell her which of the suitors she prefers. When Baptista comes in to try to break up the fight, he only angers Katherine more by showing that he favors Bianca. Both sisters leave in a huff, just before a group of visitors enters to see Baptista.

The group is composed of the gentlemen who were on their way to the pub at the end of the last scene: Gremio with Lucentio (dressed as a schoolmaster), Petruccio with Hortensio (likewise dressed as a schoolmaster), and Tranio (dressed as Lucentio) with Biondello (dressed as his servant). The introductions begin in a whirlwind of deception. Petruccio starts off, bluntly as always, by asking Baptista for the opportunity to see Katherine. In exchange, he offers a music instructor for her, the disguised Hortensio, whom he introduces as Licio. Baptista accepts the present and intends to tell Petruccio as kindly as possible that Petruccio must be crazy to want to see Katherine, when Gremio, who cannot stand being upstaged, interrupts him. Gremio presents his own schoolmaster, the disguised Lucentio, whom he calls Cambio, a master of classical languages. Baptista accepts the gift and then hears from Tranio, who, pretending to be Lucentio, presents his own gift of books and a lute, in exchange for the permission to see and woo Bianca.

The two phony schoolmasters leave to ply their trades on Bianca, while Petruccio presses Baptista further for information about Katherine. After confirming that a substantial dowry will accompany his successful wooing of Katherine, Petruccio assures Baptista of his abilities. Hortensio cuts him off by returning, his head now bleeding—apparently, when Hortensio attempted to teach Katherine how to play the lute, she promptly took the instrument and smashed it over his head. Undaunted, Petruccio waits for Baptista to send Katherine out to see him. He decides to adopt the tactic of calling her “Kate” and good-naturedly contradicting everything she says.

Abrasive as always, Katherine tears into Petruccio from the moment he sets foot in her room. Petruccio’s quick wit, though, proves equal to hers, and Katherine, used to skewering the slower-witted men by whom she is surrounded, finds his aptitude for sparring highly frustrating. They engage in a lengthy verbal duel with elaborate puns, each one constructing a new metaphor from the other’s comments—Kate’s puns generally insult or threaten, but Petruccio twists them into sexual innuendo. Eventually, she becomes so enraged that she hits him, but he continues the game just the same, saying that he will marry her whether or not she is willing: “will you, nill you, I will marry you” (II.i.263).

When Baptista, Gremio, and Tranio enter to check on Petruccio’s progress, he claims that they have already agreed upon Sunday as the wedding day. Kate, shocked, contradicts him, but he ignores her objections and insists to the other men that Katherine cannot keep her hands off him. Strangely, Kate remains silent after this remark, and when Petruccio again claims that they will marry on Sunday, she says nothing, and they both leave.

After recovering from the shock of the hasty arrangement they have just witnessed, Gremio and Tranio immediately move to the matter of Bianca, who suddenly will be available after Sunday. Baptista says that whichever of the suitors can best ensure that Bianca will be provided for when she is a widow—in other words, whichever has the greatest wealth—may have her hand. Having assumed the false, unknown identity of Lucentio, Tranio is able to claim that he has limitless funding and simply guarantees ten times whatever Gremio offers. Baptista agrees to award Bianca to Lucentio as soon as his father can guarantee the wealth that he has claimed. Tranio, confident of his ability to play the part of Lucentio, believes he can produce Lucentio’s father as well.

Although the turning point of the action in a Shakespearean play usually occurs in the third act, here, in Act II, we already witness an emotional turning point for Kate when she fails to refute Petruccio’s assertion that they are engaged. Her silence at the end of this scene is remarkable. She has always used her tongue liberally to get her way, and here, when Petruccio seems to force marriage upon her, a decision that will affect the rest of her life, she lapses into silence. As before, when Baptista is present, the men ignore Kate, talking about her, not to her. In the same way, Petruccio treats her like she doesn’t exist when telling the others of their wedding plans. In fact, Petruccio thinks so little of what Kate replies that Gremio, fearing that Petruccio’s presumptuous confidence will impede his own chances of marrying Bianca, reiterates what Kate initially says to him: “Hark, Petruccio, she says she’ll see thee hanged first” (II.i.292). Inexplicably, when Petruccio persists, she actually complies.

Kate’s compliance with Petruccio’s decree may surprise us, but if we consider her as essentially misunderstood by the other characters, her behavior may appear more understandable. The men view her as a shrew, but they care very little about the origins of her shrewish nature. Nor do they wonder why Kate chooses to maintain her behavior. If her temper results from her frustration with the dim-witted qualities of the men around her, one easy explanation for her acceptance of Petruccio would be that he is her equal in wit and willpower. Indeed, compared to the other suitors who simply run from Kate’s temper, Petruccio fires a countering shot at each and every one of her arrows. Petruccio displays an admirable wit, and, in this verbal duel of puns and double entendres, we see quintessential Shakespeare inventiveness and linguistic skill. On the other hand, Petruccio does not respect Kate, or at least he pretends to disrespect her for the sake of the game. It seems strange that Kate’s independent personality would be willing to accept someone who gives her just as little credit as did the other suitors merely because he can match her wit.

At the beginning of the scene, though, Kate shows that she may have another motive for complying with Petruccio. When fighting with Bianca, she admits that she is jealous because of the fact that her sister is being courted and will probably soon marry. She says to Baptista: “She [Bianca] is your treasure, she must have a husband. / I must dance barefoot on her wedding day, / And for your love to her lead apes in hell” (II.i.32–34). (Leading apes in hell refers to the lot of women who die old maids, unmarried.) Here, Kate appears to be frustrated by the fact that her biological clock is ticking, but she finds herself caught in a vicious circle: she hates the suitors because they do not want to marry her, and men will not marry her because she makes it so obvious that she hates them. Perhaps Petruccio’s indefatigable nature has broken the cycle, or it may be that he is the first man to speak kind words to her, even if he did not truly mean them.

Whereas Hortensio and Gremio make it very clear when they are put off by Kate’s sharpness, Petruccio amiably covers it up with praise: “For she’s not froward, but modest as the dove. / She is not hot, but temperate as the morn” (II.i.285–286). After Petruccio invokes this simile, Kate’s resistance falters. It will return, but Petruccio clearly did not miss the mark with his strategy, which capitalizes on her need for acceptance. In this scene, Kate shows that she is doubly miserable in her existence as an unmarried girl, having alienated herself from the society she despised. It may be that marriage represents a new beginning for Kate, a chance to take on a new social role and possibly find a more satisfying way to integrate -herself into her surroundings.