Computer modeling of the behavior of materials is very important for the development of additive technologies at the present stage. This article is devoted to a review of models that can and should be used for numerical modeling of material deformation as applied to additive technologies in the process of layer-by-layer synthesis, as well as an exposition of the Cosserat elastoplastic model, the rationale for its application for modeling plastic deformation in structurally inhomogeneous materials such as polymers for additive manufacturing.