In a recent paper [J. Math. Phys. 31, No. 10, 2454-2458 (1990; Zbl 0726.70011)], R. Tikekar has proposed a relativistic model for superdense stars. In this model, the hypersurfaces generated by \(\{t= \text{constant}\}\) have the geometry of the 3-spheroid which gives the solutions a clear geometrical characterization. The authors have obtained new solutions to the field equations for the Tikekar model. They have succeeded by imposing spheroidal symmetry. The authors are hopeful that the use of other symmetries may generate new solutions.