Computer models of the quasi-static rigid-die and electrohydroimpulse sheet metal drawing processes have been developed in the LS-DYNA finite-element complex. The applicability of the proposed impulse pressure law for simulation was shown. A comparative evaluation of quasi-static rigid-die and electrohydroimpulse sheet metal forming processes was carried out. Moreover, estimation of the main factors leading to defect occurrence during electrohydroimpulse sheet metal drawing was done. Total impulse duration, relative pressure increase time and impulse amplitude were varied in the simulation of impulse drawing. Thus, estimation of the spherical die filling rate, wrinkling and cracking tendencies and the influence of the recoil effect on sheet metal blank dimensions were carried out by finite-element analysis. As a result, the most favorable impulse pressure parameters were determined. These parameters contribute to spherical die filling and reducing the probability of occurrence of different defects.