The paper presents the results of numerical studies based on a mathematical model determined by the stress-strain state examination method. Numerical computations for two steel grades, namely h40 and C45, were made at similar strain and process rate parameters. as a result of the studies, the distribution of elastic and plastic zones was obtained, while the tube hollow drawing force was verified experimentally. The distribution of longitudinal, radial and circumferential stresses and, after the drawing operation, the distribution of residual stresses in the tube cross-section were also obtained.