The problem of calculating the eigenfrequencies of bound bending and torsional vibrations of a rectangular cantilever plate made from an elastic anisotropic composite is considered. The asymptotic behaviour of mostly bending and mostly torsional vibration frequencies for the composite cantilever plate with the length infinitely increasing is analyzed under binomial and trinomial representations of the approximate solution. The obtained asymptotics of the frequencies of mostly torsional vibrations confirms the necessity of taking account of the plate bend in the transverse direction.