Abstract: Based on the constructive interference theory of elastic waves in elastic plate, employing effective medium method for random medium, the propagation of SH waves in a heterogeneous material plate with randomly distributed fibers is investigated. The effective wave number in the heterogeneous medium is presented. By satisfying the boundary conditions at the upper and lower surfaces of the layer, the dispersion relation in the elastic layer is obtained. As an example, the dispersion curves for the first four modes are graphically presented. It is shown that the dispersion curves in heterogeneous elastic layer are quite different from those in homogeneous elastic layer. The effects of the properties contrast ratio of fiber to matrix, the volume fraction of fibers and the ratio of the plate thickness to the radius of fibers on the dispersion curves in the plate are analyzed.