The search for technological options for obtaining a solid assembly with small values of deformations determines the need to use a combined thermal effect on the zone of connection of extended elements made of carbon steel. Prediction of residual stress values occurring in the heat-affected zone of an assembly is difficult because of the influence of a significant number of factors: heat removal conditions, volume and material properties, etc. To calculate the residual stresses in the material, an experimentally confirmed mathematical model was used, containing viscosity and strain hardening parameters in the plastic flow criterion.