Pressure welding (PW) is an advanced method for obtaining solid phase joints (SPJs). Using physical and finite element modelling (FEM) it is shown that PW under superplasticity conditions provides SPJs between dissimilar cast single-crystal intermetallic and deformed polycrystalline heat-resistant Ni-based superalloys. Special attention is paid to exclude the stagnant zones in the solid phase joining region using surface relief. The results of physical modelling and FEM are in qualitative agreement. It is revealed that the surface relief can decrease the stagnant zone and increase localisation of deformation in the joining region, which helps to improve the joining quality. A monotonous change in microhardness in the joint zone is shown.