A number of the standard numerical methods used to solve the two-dimensional shallow water wave equations are unstable if their domains contain dry beds. We present a robust and stable finite volume method based on an unstructured triangular grid which can deal with dry beds. In particular we present a second-order explicit method which deal with dry beds in a stable manner. The method uses a simple approximate one dimensional Riemann solver due to Toro which provides the basis for an efficient implementation.