A source for Shakespeare's sub-plot was first identified by Alfred Tolman in 1890 as Ludovico Ariosto 's I Suppositi , which was published in 1551. George Gascoigne 's English prose translation Supposes was performed in 1566 and printed in 1573.  In I Suppositi , Erostrato (the equivalent of Lucentio) falls in love with Polynesta (Bianca), daughter of Damon (Baptista). Erostrato disguises himself as Dulipo (Tranio), a servant, whilst the real Dulipo pretends to be Erostrato. Having done this, Erostrato is hired as a tutor for Polynesta. Meanwhile, Dulipo pretends to formally woo Polynesta so as to frustrate the wooing of the aged Cleander (Gremio). Dulipo outbids Cleander, but he promises far more than he can deliver, so he and Erostrato dupe a travelling gentleman from Siena into pretending to be Erostrato's father, Philogano (Vincentio). However, when Polynesta is found to be pregnant, Damon has Dulipo imprisoned (the real father is Erostrato). Soon thereafter, the real Philogano arrives, and all comes to a head. Erostrato reveals himself, and begs clemency for Dulipo. Damon realises that Polynesta is truly in love with Erostrato, and so forgives the subterfuge. Having been released from jail, Dulipo then discovers he is Cleander's son.  An additional minor source is Mostellaria by Plautus , from which Shakespeare probably took the names of Tranio and Grumio. 
Baptista is enthusiastic about Petruchio’s suit because the feisty Katherina is a burden to him and is continually quarrelling with her sister and with him. Petruchio will not be put off as he woos Kate and he fixes their wedding day. At the church, where Kate unwillingly awaits him, Petruchio arrives in an absurd outfit and after the ceremony he leaves for Verona immediately, with his new wife. On reaching there Kate is mistreated by Petruchio and his servants, and is denied food and sleep. To teach her to obey him Petruchio does not allow her new clothes or a hat. Eventually, worn down by her husband’s relentless eccentricity, Kate submits and accepts all his eccentricities. They set off to visit her father in Padua.