Abstract This paper deals with the solvability and numerical solution of contact problem with a local visco-plastic friction in the visco-plastic Bingham rheology. The model problem discussed represents a simple hydro-mechanical model of the global project on a security of regions endangered by great hurricanes and deluges. The main goal of the idea of this project is to connect the climatic observations and the corresponding climatic models with the thermo-hydro-dynamic and the thermo-hydro-mechanic models, with the possibility to estimate future destructions of such endangered regions with landslides of unstable slopes. The investigated mathematical model is based on the visco-plastic Bingham rheology. The numerical approach is based on the semi-implicit scheme in time and the FE approximation in space. The algorithm is shortly discussed.