A new analyticalรnumerical approach to investigation of the response of multilayer plates to impulse loading is described in this paper[ The plate|s behaviour is described by the equations of the three!dimensional elasticity theory[ According to the approach being proposed\ the sought for functions included in the system of equations and the boundary and initial conditions are presented as Fourier series expansions in the tangential directions[ The derivatives of these functions in the transverse direction are replaced by their _nite!di}erence presentations[ As a result of such transforms\ the problem of vibration of a multilayer plate is reduced to integration of a system of ordinary di}erential equations with constant coe.cients[ Integration is performed by expansion into the Taylor|s series[ The possibilities of the approach proposed and the validity of results obtained is illustrated by several examples of calculating vibration processes and the processes of propagation of elastic waves[ A comparison of the results obtained on the basis of other approaches has been performed[ ร 0888 Elsevier Science Ltd[ All rights reserved