We consider exact models for dense relativistic stars with anisotropic pressures and containing Buchdahl-type spacetime geometry. The Buchdahl condition can be transformed to an Euler-Cauchy equation for the gravitational potentials. We solve this condition to find a new exact solution to the Einstein field equations with anisotropic matter distribution. We show that the exact solution produces a realistic model of a compact relativistic star satisfying all physical requirements. The regularity, equilibrium, casuality, stability, energy conditions and compactness limits for a well behaved compact sphere are satisfied.