An exact analytic solution of Lamb's problem is presented with no approximation or restriction for material parameters or source observer geometries. The transient-wave field for a directional point force normal to the surface of an elastic half-space is given in terms of its constituent components: the body waves, the surface wave, and the near field. In contrast to other known solutions, ours enables us to characterize these wave phenomena separately.
Some outstanding features should be mentioned: the singularities appearing in the Green's function solution of the problem are integrable. The transient-wave solution presented is well-suited for numerical computation.