In this study, we present a newly developed method for the estimation of surface flow paths on a digital elevation model (DEM). The objective is to use a form-based algorithm, analyzing flow over single cells by dividing them into eight triangular facets and to estimate the surface flow paths on a raster DEM. For each cell on a gridded DEM, the triangular form-based multiple flow algorithm (TFM) was used to distribute flow to one or more of the eight neighbor cells, which determined the flow paths over the DEM. Because each of the eight facets covering a cell has a constant slope and aspect, the estimations of – for example – flow direction and divergence/convergence are more intuitive and less complicated than many traditional raster-based solutions. Experiments were undertaken by estimating the specific catchment area (SCA) over a number of mathematical surfaces, as well as on a real-world DEM. Comparisons were made between the derived SCA by the TFM algorithm with eight other algorithms reported in the literature. The results show that the TFM algorithm produced the closest outcomes to the theoretical values of the SCA compared with other algorithms, derived more consistent outcomes, and was less influenced by surface shapes. The real-world DEM test shows that the TFM was capable of modeling flow distribution without noticeable ‘artefacts’, and its ability to track flow paths makes it an appropriate platform for dynamic surface flow simulation.