The two-dimensional (2D) equations for thin elastic plates are used to study extensional motions of a sandwich plate with weak interfaces. The interfaces are governed by the shear-slip model that possesses interface elasticity and allows for a discontinuity of the tangential displacements at the interfaces. Equations for the individual layers of the sandwich plate are coupled by the interface conditions. Through a procedure initiated by Mindlin, the layer equations can be written into equations for the collective motion of the layers representing the extensional motion of the sandwich plate, and equations for the relative motions of the layers with respect to each other representing the symmetric thickness-shear motion of the sandwich plate. The use of plate equations results in relatively simpler models compared to the equations of three-dimensional (3D) elasticity. Solutions to a few useful problems are presented. These include the propagation of straight-crested waves in an unbounded plate with weak interfaces, the reflection of extensional waves at the joint between a perfectly bonded sandwich plate and a sandwich plate with weak interfaces, and the vibration of a finite sandwich plate with weak interfaces.