  A general formalism developed few years ago to model polytropic Newtonian
stars with anisotropic pressure is applied to model stars for which, both,
radial and tangential pressure satisfy polytropic equations of state. We obtain
the corresponding Lane--Emden equation, and integrate it for a wide range of
values of the parameters, thereby illustrating the effects of the pressure
anisotropy on stellar objects. We calculate Chandrasekhar mass for a white
dwarf and compare it with previous results. Finally, prospective applications
to some astrophysical scenarios are discussed.
