This paper describes a 3D structure-imitation computer model of evolution of the powder compactduring sintering and recrystallizationwithout nucleation. At the initial stages ofthe evolution processes (sintering until a mosaic structure of boundaries is formed) the model particles are spheres, and two-particle interaction laws control their evolution. During sintering the degree ofmutual penetration ofthe particles increases, regions where spherical particles are wholly facetted by contacts with neighboring particles are formed and grow. These particles are described using the formalism of Voronoi radical polyhedra, and grain growth laws govern their evolution. The model predicts the time dependencies of the following structure parameters of the polyhedra: average polyhedron size and dispersion, total surface of the facets of the polyhedra and total length of the edges of the polyhedra.