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The present paper is devoted for modeling the temperature and residual stress fields evolution in a thermoviscoelastic cylinder that grows layer by layer, and to what extent does the degree of viscosity affect the residual stress reduction. The essence of this mathematical model is to analyze a series of initial-boundary value problems that describe the steps of the growth process, to give qualitative clarification for residual stress accumulation and distortion of final geometric shape. At each step, the domain in which the physical quantities are studied, increases due to adding a layer. The inductive heating by skin effect phenomena is applied during the additive process to minimize residual stresses intensity which appears in additive manufacturing, particularly in CLM or CLS technological processes. The temperature field on the growing surface is analyzed numerically for Titanium and Copper materials.