The spheropolyhedra method has been used earlier for efficient and accurate molecular dynamics simulations of granular matter with particles with complex shapes. Also the Voronoi construction is a tool of proved utility for the virtual representation of powders and grains. In this paper a technique that combines the two methods and provides a framework for the study of the three-dimensional mechanical behavior of granular matter is proposed. In order to understand the capabilities of the new method, a number of computer simulations of the cubic (true) triaxial test, measuring the mechanical behavior of packing of particles, is carried out. Results from tests with packing of complex-shaped particles represented by "Voronoi particles" are compared with corresponding results of packing of spherical particles. Features such as the saturation value for the macroscopically observed coefficient of friction, as reported in the literature, are compared for the packing of spheres and for the packing of "Voronoi particles," showing that the difference in shape strongly affects the results. The proposed technique and simulation results can be used to help understand how the individual shape of grains affects the macroscopic mechanical behavior of granular matter such as cohesionless soils.