The majority of analysis methods for the computation of natural frequencies required by ultrasonic resonance spectroscopy is based on variational methods of approximation that incorporate basis functions with C[sup -1] continuity at every point within the domain. When used for laminated materials of different constitution, the continuous strain field implied by such approximations cannot represent true behavior at an interface between the materials. A discrete-layer theory is developed in this study which introduces piecewise approximations in the layered direction of the solid, allowing for a more accurate portrayal of the strain field. The vibrational modes can be grouped into four groups rather than the eight that are typical for an orthorhombic material. The model is used to study a seven-layer laminate composed of layers of aluminum and aramid/epoxy. Two geometries are considered: a plate and a parallelepiped. The frequencies predicted by the discrete-layer theory are compared with measurements and frequencies found using a more conventional Ritz method with the effective properties of the material. The discrete-layer frequencies tend to be slightly larger than those computed using the Ritz method for the plate and slightly lower for the parallelepiped. Implications for the use of this theory are discussed.