Large-scale fluctuations in the solar wind plasma upstream of the heliospheric termination shock (TS) will cause inward and outward motions of the shock. Using numerical techniques, we extend an earlier strictly one-dimensional (planar) analytic gasdynamic model [Barnes, 1993> to spherical symmetry to investigate the features of global behavior of shock motion. Our starting point is to establish a steady numerical solution of the gasdynamic equations describing the interaction between the solar wind and the interstellar medium. We then introduce disturbances of the solar wind dynamic pressure at an inner boundary and follow the subsequent evolution of the system, especially the motion of the termination shock. Our model solves spherically symmetric gasdynamic equations as an initial-boundary value problem. The equations in conservative form are solved using a fully implicit total variation diminishing (TVD) upwind scheme with Roe-type Riemann solver. Boundary conditions are given by the solar wind parameters on an inner spherical boundary, where they are allowed to vary with time for unsteady calculations and by a constant pressure (roughly simulating the effect of the local interstellar medium) on an outer boundary. We find that immediately after the interaction, the shock moves with speeds given by the earlier analogous analytic models. However, as the termination shock propagates, it begins to slow down, seeking a new equilibrium position. In addition, the disturbance transmitted through the TS, either a shock or rarefaction wave, will encounter the outer boundary and be reflected back. The reflected signal will encounter the TS, causing it to oscillate. The phenomenon may be repeated for a number of reflections, resulting in a ''ringing'' of the outer heliosphere. ¿ American Geophysical Union 1996