This paper presents the effect of friction in the vibration behavior between two beams in relative motion according to Timoshenko's beam theory. The current system is composed of two cantilever beams screwed together. The nonlinear behavior can be divided into two phases: stick and slip. The differential equations of motion in the two phases are presented. In one hand, the viscous damping is added in the stick phase. In the other hand, the viscous damping and the frictional force applied are added in the slipping phase. The Galerkin method is used for the solution of differential equations to transfer the system of partial differential equations to the system of ordinary differential equations.