The paper is aiming to development of an approach for arrangement of assembled parts of complex geometry in the working area of 3D printer, considering standards of 3D printing. For an analytical description of industrial products of the complex shaped, a family of convex objects is used including spheres, cylinders, spherical cylinders, cones, truncated cones and spherical discs. Using the normalized quasi-phi-function of a general convex composed object, a mathematical model of the problem is presented in the form of a nonlinear programming problem. A solution strategy is developed that combines: obtaining feasible starting points, searching for local minima and choosing the best local minimum from those found at the previous stage. Numerical examples of packing 3D parts approximated by composed convex objects from the given family are provided and illustrated with figures. This study emphasizes the importance of further research and innovation in optimization of the technological process of 3D printing.