A high-accuracy numerical solution, coupling one-dimensional shallow water and bed-evolution equations, with, for the first time, a suspended sediment advection equation, thereby including bed and/or suspended load, is used to examine two swash events on an initially plane erodible beach: the event of Peregrine & Williams (J. Fluid Mech., vol. 440, 2001, pp. 391–399) and that of a solitary wave approaching the beach. Equations are solved by the method of characteristics, and the numerical model is verified. Full coupling of suspended load to beach change for Peregrine & Williams (J. Fluid Mech., vol. 440, 2001, pp. 391–399) yields only slightly altered swash flows, depending on beach mobility and sediment response time; a series of similar final beach change patterns results for different beach mobilities. Suspended- and bed-load transport have distinct morphodynamical signatures. For the solitary wave a backwash bore is created (Hibberd & Peregrine, J. Fluid Mech., vol. 95, 1979, pp. 323–345). This morphodynamical bore propagates offshore initially, and leads to the creation of a beach bed step (Larson & Sunamura, J. Sedimentary Petrology, vol. 63, 1993, pp. 495–500), primarily due to bed-load transport. Its height is directly related to bed-load mobility, and also depends strongly on the bed friction coefficient. The shock dynamics of this bed step is explained and illustrated. Bed- and suspended-load mobilities are quantified using field data, and an attempt is made to relate predictions to measurements of single swash events on a natural beach. Average predicted bed change magnitudes across the swash are of the order of 2 mm, with maximum bed changes of up to approximately 10 cm at the bed step.