A unified theoretical treatment is presented for the calculation of displacements and stresses within multilayered media subjected to incident ultrasonic waves. The wave is supposed to be incident from water, at an arbitrary angle, upon a plate consisting of an arbitrary number of different isotropic material layers. In the first part of the analysis displacements and stresses are determined as functions of position within the plate while all layer interfaces are assumed to be rigidly bonded. A smooth interface is subsequently introduced to simulate debonding of two material layers. The composite plate is assumed to be bounded at the bottom by either a free surface, a fluid half-space or an elastic solid half-space. A byproduct of the analysis is the derivation of the reflection and transmission coefficients for the systems. Extensive numerical results are given in order to delineate the influence of the plate material orderings, layer thicknesses and interfacial conditions on the displacements and stresses within the plate. The model developed here will be of value in material characterization and in the nondestructive evaluation of advanced material applications.