The extensional and flexural Lamb waves in a sandwich plate with finite initial strains made from compressible highly elastic materials is investigated. It is assumed that the initial strains are caused by the uniformly distributed normal compression forces acting on the face planes of the plate. The cases where the compression forces are "dead" (Case 1) and "follower" (Case 2) are considered. The investigations are carried out within the scope of the piecewise homogeneous body model with the use of the 3D linearized theory of elastic waves in initially stressed bodies. Numerical results for the dispersion of the extensional and flexural Lamb waves on the influence of the initial strains and on the influence of the character of the external compression forces are presented and discussed. (C) 2010 Elsevier Masson SAS. All rights reserved.