The paper describes an algorithm for the generation of random packings of ellipsoids of revolution, which is a natural generalization of an older algorithm for the case of spherical particles and belongs to the class of collective rearrangement algorithms. It yields packings with a broad spectrum of densities and geometrical properties, aspect ratio which depend on and the various parameters controlling the motions of ellipsoids during the simulation. The ellipsoid systems obtained are characterized by second-order characteristics, namely pair correlation and orientation correlation functions. Furthermore, the constructed packings are described in a phase diagram taken from statistical physics.