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We present an algorithm to generalize a plethora of well-known solutions toEinstein field equations describing spherically symmetric relativistic fluidspheres by relaxing the pressure isotropy condition on the system. By suitablyfixing the model parameters in our formulation, we generate closed-formsolutions which may be treated as anisotropic generalization of a large classof solutions describing isotropic fluid spheres. From the resultant solutions,a particular solution is taken up to show its physical acceptability. Makinguse of the current estimate of mass and radius of a known pulsar, the effectsof anisotropic stress on the gross physical behaviour of a relativistic compactstar is also highlighted.

Anisotropic generalization of well-known solutions describing relativistic self-gravitating fluid systems: An algorithm