Riparian vegetation dynamics in Alpine rivers are to a large extent driven by the timing and magnitude of floods which inundate the floodplain, transport sediment, erode the river bed, and create and destroy suitable germination sites. Here we present a stochastic approach for studying sediment-vegetation dynamics lumped at the floodplain scale and driven by stochastic flood disturbances. The premise of the model is that floods erode riparian vegetation in the inundated part of the floodplain and expose bare sediment surfaces. In the absence of subsequent flooding these surfaces are gradually recolonized. The stochastic nature of the disturbance process and the deterministic rate of vegetation colonization are described by a Poisson arrival of floods and a process equation which treats the floodplain erosion and vegetation colonization processes, respectively. An analytical solution is developed to obtain the probability density function of the exposed sediment area. The model is applied to the Maggia River in Switzerland, where it reproduces the changes in riparian vegetation cover observed from aerial photographs with an absolute error less than 5%. The model has potential as a tool to study the impacts of changes in the disturbance regime on sediment and vegetation dynamics.