Full Text Article Also available at: 10.1007/s12043-018-1650-xWe obtain new regular exact solutions to the field equations for uncharged relativistic stellar objects with vanishing pressure anisotropy. We assume a quadratic equation of state and a choice of measure of anisotropy and a metric function defining one of the gravitational potentials. In our exact models, we regain anisotropic and isotropic results generated by other researchers as a special case. It is interesting that our results are in agreement with Minkowski space–time and earlier Einstein models. The physical analysis of the plots reveals that the gravitational potentials and matter variables are well behaved in the stellar interior. Using our model, we generate finite relativistic stellar masses which are consistent with the astronomical objects previously found by other researchers.