A new computational algorithm is introduced for packing simulation of spherical elements/particles into an imaginary container with three main possible geometries, cubic, cylindrical and spherical. The performance of the algorithm depends directly on the strategy or logic considered to solve the problem and the quality of its computational implementation. The combination of these two factors let the packing algorithm here presented and named as Octant Packing Random Algorithm (OPRA) to reduce the computation time between 2 and 127 times, when compared with the simplest or classical Packing Algorithm. OPRA is designed to reduce the number of comparisons needed to accept or reject a new position for an element/particle to be allocated into the virtual container. OPRA considers the container as if it were divided into 8 equal cells or octants limiting the overlap detection for a new position.