  We set up in detail the general formalism to model polytropic general
relativistic stars with anisotropic pressure. We shall consider two different
possible polytropic equations, all of which yield the same Lane-Emden equation
in the Newtonian limit. A heuristic model based on an ansatz to obtain
anisotropic matter solutions from known solutions for isotropic matter is
adopted to illustrate the effects of the pressure anisotropy on the structure
of the star. In this context, the Tolman mass, which is a measure of the active
gravitational mass, is invoked to explain some features of the models.
Prospective extensions of the proposed approach are pointed out.
