We present a basic continuum flow model for the emplacement of the distal rampart crater deposits on Mars. Assuming cylindrical symmetry, analytic solutions of the volume and momentum conservation equations yield time-dependent flow thickness and velocity profiles. The momentum equation has an inertial term, and a frictional resistance term that is proportional to the local volumetric flow rate. We find that only a few basic physical processes are necessary to form sharp distal ramparts. First, there must be sufficient material to form a continuum overland flow. Then, for simple choices of boundary conditions at the source of the flow, distal ramparts form naturally due to the cylindrical geometry, the inertia of the flow, and local frictional resistance. THEMIS images of rampart deposits show that the ejecta flow velocities were relatively slow, being diverted by preexisting obstacles even within ~0.2 crater radii from the rim of the parent crater. To develop inferences about rampart deposit emplacement, we require measurements of the crater radius and flow distance, and assumptions about the maximum source flow velocity and depth. We measured nine clearly expressed rampart deposits for craters with diameters of 3.4--17.0 km. The model provides estimates of the emplacement time, the rampart width, and the shape of the radial flow depth profiles. We find that modest velocities of ~27--116 m s-1, maximum source flow depths of 10--40 m, and emplacement durations of 12--31 min adequately explain the morphologies of selected rampart craters.