PorAS, a new approximate-state Riemann solver, is proposed for hyperbolic systems of conservation laws with source terms and porosity. The use of porosity enables a simple representation of urban floodplains by taking into account the global reduction in the exchange sections and storage. The introduction of the porosity coefficient induces modified expressions for the fluxes and source terms in the continuity and momentum equations. The solution is considered to be made of rarefaction waves and is determined using the Riemann invariants. To allow a direct computation of the flux through the computational cells interfaces, the Riemann invariants are expressed as functions of the flux vector. The application of the PorAS solver to the shallow water equations is presented and several computational examples are given for a comparison with the HLLC solver.