Abstract This article presents a numerical study of dispersion characteristics of some symmetric and antisymmetric composites modelled as multilayered packets of layers with arbitrary anisotropy of each layer. The authors introduce a subsidiary boundary problem of three-dimensional elasticity theory for the system of partial differential equations describing the harmonic oscillations of the composite caused by a surface load. The problem reduces to a boundary problem for ordinary differential equations by employing the Fourier transform. An algorithm of constructing the Fourier transform of the Green’s matrix of the given boundary problem is presented. The wave numbers of Lamb waves propagating in composites, their phase velocity surfaces and group wave surfaces are presented through the poles of the transform of the Green’s matrix. The authors obtain the dispersion curves for different directions and frequencies and investigate the dispersion curves and surfaces of wave numbers, phase velocities and group wave surfaces for various composites. The numerical results are then compared with the results obtained by applying other methods.