Further analytical investigations are made into the damping capability and determination of natural frequencies of laminated beams, consisting of elastic-viscoelastic-elastic layers, as a means for reducing the vibratory energy transmitted through machine foundation supports in naval vessels. An exact analytical solution is obtained for determining the natural frequencies of simply-supported sandwhich beams having no rivets at the ends. Three possible modes of vibration are shown to exist. The case of the simply- supported sandwich beam having rivets at each end is considered and the equations reduced to the solution of 12 x 12 determinant for calculation on a digital computer. An approximate method is suggested for determining the natural frequencies of sandwhich beams having any end conditions. The procedure is simple to use and is exact for simply-supported beams. A simple but approximate expression is also developed for determining the composite loss factors of sandwich beams. The procedure yields good engineering results.