Accurate representation of different parts of a mechanical system is important in construction of mathematical models for structural dynamic analysis. There are usually elements in structures - for example joints or boundary conditions - which demand more efforts for precise modeling. This is due to development of the contact mechanisms - i.e. linear or nonlinear - in normal and tangential directions of their surfaces. In this paper a method for multiple nonlinearity detection and identification is proposed. The method is applied to characterize the state of the contact mechanisms in normal and tangential directions of a nonlinear beam subjected to a frictional contact support.