A stress-strain state computer simulation of samples imitating bimetallic "disk-shaft" type parts for a gas turbine engine from dissimilar heat-resistant nickel-based superalloys during pressure welding with a shear was carried out. The simulation was performed in a two-dimensional formulation (axisymmetric problem) using the DEFORM-2D. Two shaft motion schemes, embedding of a shaft into a disk and a combination of the embedding and rotation of the shaft, were considered. To determine the influence of the microstructure of samples on the plastic deformation process in the joint zone, two combinations of nickel-based superalloys were considered: the material for the shaft in all cases was EK79 (fine-grained microstructure, 7 μm), the material for the disk was EP741NP (coarse-grained microstructure, 60 μm) or EP975 (fine-grained microstructure, 8 μm). The constitutive relations for the superalloys under study were introduced into the program as the experimental stress-strain curves obtained from uniaxial compression of cylindrical samples. Computer simulation results showed that to improve the joint quality it was preferable to use pressure welding with the embedding and rotation of the shaft. In this case two-component shear deformation was provided that lead to a relative shift of the surfaces to weld and an improvement of the conditions for the formation of physical contact. It has been established that to obtain a solid phase joint between the shaft and the disk, it is preferred to use the EK79 (shaft) and EP975 (disk) superalloys, since in this case the summarized normal compressive stresses and shear deformations are provided which leads to an increase of the joint quality.