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In a process of sheet drawing technology developing, the probability of workpiece buckling during deformation and the necessity of blank holder using to prevent corrugation, is estimated in accordance with the recommendations of the reference book. However, reference literature does not have clear recommendations, or it gives contradictory recommendations for blank holder use cases for some deformation conditions. In these cases, problem solving requires additional experimental research. Possibility and efficiency establishing of computer simulation using DEFORM environment of axisymmetric drawing processes to forecast the buckling of a thin-sheet workpiece during deformation. Technological processes of sheet drawing with a high probability of workpiece buckling were investigated by means of finite element computer simulation in DEFORM 3D. Research has established that simulation of thin-sheet workpiece drawing process in DEFORM 3D, allows to visualize the process of corrugation, and predict workpiece buckling with high probability, provided that the deformation occurs relatively simple geometry of the workpiece and deforming tool. In more complex deformation conditions, the experiments results, and computer simulation may differ (simulations may not indicate corrugation). This somewhat complicates corrugation prediction, but the problem is solved by an extended analysis of the stress-strain state and workpiece behavior in the deformation zone. The emergence of areas in the workpiece with an unpredictable and uncontrolled contact loss of the workpiece material with the deforming tool, or appearance of areas with significant irregular velocity of workpiece points movement, clearly indicates problem areas with high probability of corrugation in the real sheet drawing process. Obtained results allow to increase the efficiency of expecting places of corrugation appearance prediction by means of computer simulation of sheet drawing process in the DEFORM 3D environment. [ABSTRACT FROM AUTHOR]