Modeling of the structure of powder materials with dense packing of nonspherical particles is considered. A numerical method is suggested based on an original computer model of packing for particles of complex shape (spherical polyhedra that are considered as smooth convex polyhedrons). Numerical experiments are provided for packing of particles with lamellar, cylindrical, and cubic shape. A dependence is established for coordination number and packing porosity on particle surface area and shape.