Аннотация:Mechanical design of additive manufacturing (AM) fabricated viscoelastic parts under consideration. Such a design is of great importance for obtaining final products with desired shape and strength which are determined by their stress-strain state. Mathematical model of model of viscoelastic solid which grows due to the process of additive manufacturing is proposed. Complete system of boundary value problem equations is obtained. A method for solving formulated boundary value problem is developed. Qualitative conclusions concerning the behavior of growing solids are presented.