We present a simple analytical method to study birefringence and polarization mode dispersion (PMD) of elliptic-core fibers with uniform or differential stress in the fiber cross section. The model takes account of both geometrical and stress birefringence, simultaneously. It is found that neglecting the geometrical birefringence, even under the weakly guiding approximation, can lead to significant errors in the calculation of PMD and the zero PMD wavelength. It is also found that one can obtain zero PMD in the single-mode region even by applying a suitable differential stress along the major axis. This is very attractive since then the geometrical and stress birefringences add up to give increased total birefringence.