<p>This paper addresses the problem of the rolling motion on a plane of an unbalanced ellipsoid of revolution with symmetrically truncated vertices. The problem is considered using the model of a rubber rolling. By the rubber model of rolling we mean the rolling of a body without slipping nor twisting at the point of contact. First integrals are presented and a reduction to quadratures is performed. Partial solutions of the resulting system are found and it is shown that they correspond either to the rolling motion of the body in a circle or to an equilibrium point. A gyroscopic function is analyzed to examine bifurcations of partial solutions and to carry out a classification of all types of bifurcation diagrams according to parameters.</p>