This thesis deals with a contact problems between dissimilar materials in geotechnics, specifically the interface between footing and soil. There are two groups of interface elements studied, the zerothickness and thin-layer. Additionally there is analyzed the Augmented lagrange approach which is a part of the broader family of multi-freedom constraint solutions. The analysis is performed in commercial softwares such as MATLAB, Optum G2 and PLAXIS 2D. Furthermore the load bearing capacity is analyzed. The results are validated using the Chris Martin solution.