In the first phase of the detailed nodelling of cross-shore sediment transport under random waves a model is constructed which adopts a vertically integrated transport description for sheetflow situations. The formulation of the transport as a function of the instantaneous velocity field is based on the approach of Bailard (1981). This approach assumes in essence simply that the instantaneous transport is proportional with some power of the instantaneous near-bottom velocity. Implementation of this transport description in a time-dependent model requires a formulation of the time-mean and some low order moments of the near-bottom velocity field. An ad-hoc formulation based on a monochromatic, second order Stokes wave representation is presented. A numerical research model, based on the above formulations, is described and limitedly checked on its performance on the basis of an available field data set. Some consequences for further study are indicated