The present work is based on previous research on the one-dimensional (1D) analysis of the hydrogen diffusion process, and proposes a numerical approach of the same phenomenon in two-dimensional (2D) situations, e.g. notches. The weighted residual method was used to solve numerically the differential equations set out when the geometry was discretized through the application of the finite element method. Three-node triangular elements were used in the discretization, due to its simplicity, and a numerical algorithm was numerically implemented to obtain the hydrogen concentration distribution in the material at different time increments. The model is a powerful tool to analyze hydrogen embrittlement phenomena in structural materials.