The work reported in this paper describes the behavior and prediction of damping properties of the 3D composite laminated engine mount shell structure. The shell structure has a shape of box with four vertical and two horizontal plates with the thickness of 15mm and 20mm respectively. For more accurate prediction of the structural behavior, many researchers have incorporated the time dependent property of the material into their field of studies. In this article the finite element approach utilizes the concept of viscoelastic damping, which is carried out by direct integration. This paper describes the potential application of composite material as a damper device because of its damping, high stiffness and low weight properties, which favor the use as engine mount in submarine and ships where weight is the highest priority.