A deep drawing apparatus is provided in which a sheet material is subjected to optimal heating and cooling, whereby the limiting draw ratio is increased and a product can be worked more deeply, and uniformity of the sheet thickness of the product can be controlled. This apparatus includes: a punch 2 for subjecting a sheet material 9 to deep drawing; a die 3, used along with the punch, for forming the sheet material and subject the same to deep drawing; an anti-wrinkling component 4 for preventing wrinkling around the periphery of the forming portion in the sheet material; an induction heating coil 5 for directly heating the sheet material at a portion supported by the anti-wrinkling component; a heating controller 6 for controlling the amount of heating of the sheet material by the induction heating coil; and cooling means 21 to 23 for cooling the sheet material at the portion formed by the punch.