A press for producing hollow articles by deep drawing of a blank comprising a high-pressure vessel, a die accommodated in said high pressure vessel and having a drawing rib engageable with a blank, a punch accommodated in said high pressure vessel, a punch-actuating hydraulic cylinder having a piston rigidly connected with said punch, a clamp formed with a collar for hermetic separation of a central portion of the blank from a peripheral portion and positioned opposite the drawing rib of the die, the die having an end surface which forms, together with an end surface of the clamp and with an inner surface of the high-pressure vessel, an annular high-pressure chamber wherein is positioned the peripheral portion of the blank, a high-pressure chamber of an intensifier communicating with said annular high-pressure chamber, a pressure regulator for controlling pressure in the annular chamber and incorporating a second hydraulic cylinder and a second piston whose cavity is brought in communication with a rod cavity of the punch-actuating hydraulic cylinder, an appliance for setting pressure in the annular high-pressure chamber, said appliance being fixed on a rod of the second piston, and a regulator of pressure created in the high-pressure chamber of the intensifier and acting on the peripheral portion of the blank, said pressure regulator having a sensitive element brought in contact with the pressure setting appliance whereby the pressure in the annular high pressure chamber is varied in accordance with movement of said punch to thereby control the quality of the drawn blanks.