Propagation of P and SV waves in an elastic solid containing randomly distributed inclusions in a half-space is investigated. The approach is based on a multiple scattering analysis similar to the one proposed by Waterman and Truell for scalar waves. The characteristic equation, the solution of which yields the effective wave numbers of coherent elastic waves, is obtained. Formulae are derived for the effective wave numbers in a dilute random distribution of identical scatterers. They generalize the formula obtained by Waterman and Truell for scalar coherent waves. It is shown that P and SV waves are coupled for non circular cylinders but uncoupled for circular cylinders.