The interaction of the solar wind with the two-component interstellar medium consisting of thermal plasma and galactic cosmic rays is studied numerically using a soft fitting technique based on the high-resolution Godunov scheme and the physical process splitting method. Mutual influence of plasma and cosmic ray components on the solar wind termination is considered. It is shown that cosmic rays can considerably modify the shape and structure of the solar wind termination shock and the bow shock, and change the positions of the heliopause and bow shock if no H atoms are taken into account. ¿ 2000 American Geophysical Union