Vibration damping is an important phenomenon in the field of engineering design while predicting the dynamic analysis of the most of the structures. It is one of the typical dynamic responses of structural members, which allows the members fail due to larger amplitudes. Composite materials are replacing conventional structural materials due to attractive, superior mechanical properties such as high strength to weight ratio, high modulus, high corrosion resistance and good fatigue resistance. Composite materials possess high degree of material damping compared with conventional materials. One of the advanced technique employed to safe guard against the severe intensity of vibrations by controlling the dynamics of the structures is the provision of enhancing energy dissipation by the design of a constrain layer. When a constrain layer is made of a non actuating stiff layer of material introduced in the structure, say a viscoelastic material called a PCLD (Passive constrained layer damping). In the present work, an analytical solution for damping of a FRP (Fiber reinforced polymer) plates with a single or double interleaved viscoelastic layers in is obtained. Ritz method is employed to predict the damping nature of the plate under several boundary conditions. Specific damping capacity and a loss factor are deduced from the method of energy formulation for viscoelastic layers interleaved in laminated fiber reinforced plate. The loss factor of constrain layered plate is calculated as a function of fiber orientation in its orthotropic layers. An isotropic constrain layers are configured at midplane, symmetric, asymmetric and outer positions across the thickness of the plate. A parametric study also carried out to observe the effect of position of a constant thickness viscoelastic layer on the damping characteristics of passively constrain orthotropic plate.