In an axially symmetrical single-mode optical fiber, the polarization plane of the propagated HE11 mode is subject to unstable rotation due to slight changes in ambient conditions. Such an instability can be prevented by making the refractive index distribution in the fiber axially nonsymmetrical. This paper describes a two-dimensional, vectorial-wave finite-element method calculation of the propagation characteristics of such axially nonsymmetrical fibers. It is an improved version of Yeh's program; the field outside the central core region is expanded by a series of modified Bessel functions. Some numerical examples are described.