This paper deals with the problem of packing elongated cylindrical nanostructures, such as carbon nanotubes (CNTs), into a bounded three-dimensional domain, taking into account their spatial positions and orientations. The motivation is forced by experiments that demonstrate that the orientation of carbon nanotubes influences the material's mechanical, electrical, and thermal properties. To consider these peculiarities, we introduce a geometric mathematical model that extends standard non-overlap conditions by adding angular constraints depending on orientation. The formulation is a mixed-integer nonlinear programming (MINLP) problem, where continuous and binary variables are used. It makes it possible to adjust the number of cylinders and rotation angles with respect to axis directions and manage how cylinders are oriented to each other. The solving approach uses decomposition into subsets, starts with block-coordinate initialization, and then applies continuous optimization using the IPOPT solver. Two numerical examples are given, one considering almost parallel alignment, which is essential for conductive composites, and another showing random orientations, typical for porous or entangled structures.