The actual efficiency of constrained viscoelastics layers is sometimes misunderstood. To study in depth this configuration, a theoretical approach has been developed by generalizing Ungar's formulation [E. E. Ungar, J. Acoust. Soc. Am. 34, 1082--1089 (1962)]. The shear effect, ``in-plane'' motion, and flexion are taken in account into the viscoelastic layer while only flexion is considered for the metallic layer. By expressing ``in-plane'' and shear displacements in terms of transverse displacements, a linear system is obtained. Radiation impedances are calculated via Nelisse's model [H. Nelisse et al., J. Sound Vib. 198(4), 485--506 (1996)]. The theoretical results have been systematically validated experimentally with a dedicated setup. Basic configurations of interest are: basic plate, basic plate and constrained viscoelastic layer with total or partial covering under or not under the excitation forces. A case of nonmetallic (fiber resin) material is also studied, leading to very interesting results. Finally, an optimization study brings new meaningful design possibilities.