In the work, on the basis of the analysis of publications, existing approaches to the numerical modeling of additive processes of product formation are shown. The work itself is devoted to the study of the influence of parameters of the process of surfacing wire materials on the formation of residual deformations in parts. A mathematical formulation of the non-stationary thermomechanical problem is presented, and algorithms for solving the problem using the technology of birth and death of finite elements in the ANSYS package are described. Verification of the model created by the finite element was carried out on the basis of data from the experiment on surfacing a multilayer sample. The effect on the level of residual warping of the following process parameters was studied: the exposure time before the next layer was deposited; the motion path of the burner; ambient temperature. It is shown that the change in ambient temperature is the most effective way to reduce the residual distortions of the form.