The purpose of this study is to verify the vibration and damping characteristics of a partially-layered elastic-viscoelastic-elastic structure both theoretically and experimentally. The fourth-order differential equations of motion are derived for the transverse vibration of a three-layered sandwich beam with a viscoelastic (or adhesive) core layer. The transverse displacements of the constraining layer and the base beam are assumed to have different parameters. Both the transverse normal strain and the longitudinal shear strain of the viscoelastic core layer are included in the equations of motion. The solution to the resulting equations is obtained by solving a boundary value problem. Numerical analysis of the equations and experimental measurements is illustrated by a cantilever beam in transverse vibration. The vibration and damping effects of completely and partially covered beams are investigated and the effect of the position changes of partial coverage is intensively analyzed.