We developed a two-dimensional steady state numerical model that can describe the modulation of galactic cosmic rays in an arbitrarily shaped heliospheric outer modulation boundary. The model is based on the well-known Parker transport equation for cosmic rays and incorporates: (1) gradient and curvature drift effects including drift along a wavy neutral sheet, (2) adiabatic energy changes, (3) diffusion parallel and anisotropic diffusion perpendicular to the heliospheric magnetic field, and (4) outward convection due to a latitude-dependent expanding solar wind plasma. The model is described together with results illustrating the effects of an asymmetric heliospheric boundary on the spatial and energy variations of galactic cosmic ray protons throughout the heliosphere. The cosmic ray distribution in the inner heliosphere was only marginally altered, but significant changes were found beyond ~30 AU, especially in the upwind direction. Concerning the energy dependence of these effects the maximum cosmic ray redistribution occurred at ~50 MeV. At energies of >5 GeV the effects became insignificant. Assuming a highly asymmetric heliosphere, we calculated a longitudinal gradient of 0.4% deg-1 for 1 GV protons at 50 AU, which may be considered an upper limit. ¿ 1998 American Geophysical Union