The phenomenon of floodplain inundation can be modeled using the shallow water equations. Since during the inflow phase the area is initially dry, the shallow water equations must be solved in a domain with variable geometry. As a result, the solution domain is bounded by propagating wave front that separates dry and wet areas. In this case, very small depths occurring at this front give high velocities, which can then lead to negative values of depths and numerical instability. The above problems resulting from the application of the shallow water equations for simulation of the flow over floodplain can be avoided by using the simplified diffusive wave model. During the flood wave propagation over floodplain, the part of water volume can infiltrate into the soil. In the work it is assumed that the infiltration process is described by the Horton equation, which is coupled with a diffusive wave equation by source term. In order to solve the two-dimensional diffusive wave equation the splitting methods with regard to the directions and physical processes are applied, whereas a modified finite element method is used for spatial discretization. This approach leads to an efficient and stable numerical algorithm, which also ensures an adequate accuracy required during simulation of floodplain inundation.