An analytical model for the lateral vibration of beams with a bonded lap joint and partial layered dampers has been proposed in this paper. Both shear and normal forces acting along the interface between the elastic and viscoelastic layers were considered in the vibration analysis. Analytical results were compared with those obtained by a finite element method. Effects of the size and location of layers in partial dampers on system loss factor($eta_s$) and resonant frequency($omega_r$) were studied. which showed that partial dampers adhered to the site exhibiting the maximum amplitude of vibration were most influential in the increase of $eta_s$ and the decrease of $omega_r$. Specific system loss factor( $eta_s$ divided by total mass of system) was also evaluated in the analysis.