Interest in slow-mode shocks in space physics applications has increased in recent years. These shocks, which can arise from the steepening of linear slow-mode magnetohydrodynamic waves, might form ahead of objects moving through a magnetized, highly conducting gas at speeds greater than the slow-mode speed. In particular, slow shocks are the only shocks possible for speeds between those of the slow and fast modes. This appears to be the speed range, for example, of many and perhaps most coronal mass ejections. Despite the interest in and detection of slow-mode shocks in the heliosphere, there appear to date to be no calculations of flows involving slow shocks. Basic properties like shock configuration and standoff distance are therefore unknown, although several authors have pointed out that slow shocks should extend upstream of the obstacle giving rise to the shock. This paper presents a simple method for computing slow shock flows in an infinitely conducting plasma, based on the solution of a free boundary problem for the shock configuration that matches a post shock potential flow to a uniform preshock flow. Such potential-flow methods have been used in ordinary gasdynamics to obtain crude approximations to blunt-body flows containing shocks; arguments given here suggest that the potential-flow approximation should be more accurate in the case of slow MHD shocks. The method is applied to shocks arising from flow about spherical and paraboloidal obstacles. A parametric study of shock formation as a function of sonic and Alfv¿n Mach numbers shows standoff distance increasing as either Mach number decreases. Streamlines and shock configurations for several slow shock flows are also presented. ¿American Geophysical Union 1987