  Spherically symmetric relativistic stars with the polytropic equation of
state, which possess the local pressure anisotropy, are considered in the
context of general relativity. The modified Lane-Emden equations are derived
for the special ansatz for the anisotropy parameter $\Delta$ in the form of the
differential relation between $\Delta$ and the metric function $\nu$. The
analytical solutions of the obtained equations are found for incompressible
fluid stars. The dynamical stability of incompressible anisotropic fluid stars
against radial oscillations is studied.
