The paper considers a relaxation technique in a sphere packing problem with a specific focus on study of materials structure. The objective is to maximize the number of non-overlapping spheres in a cylindrical container regarding a given ratio of the different radii spheres appearance. Two scenarios are discussed to examine an effect of relaxing constraints on the packing spherical objects. In the first scenario, spheres packed within the container while adhering to strict containment conditions. The second scenario violates the containment condition by allowing spheres intersect the container boundary. This relaxation provides a more accurate estimation of the material's porosity by eliminating artificial effects caused by boundary constraints. A fast heuristic approach is developed that combines a modification of the block coordinate descent algorithm and a new cylindrical lattice decomposition strategy. Computational results are presented and illustrated with examples for two scenarios. The findings highlight the importance of the proposed techniques in materials structure studies and can be extended to packing particles of various shaped.