When the Alekseev-Mikhailenko method was used for the exact numerical solution of Lamb's problem, a new strong nongeometrical arrival, denoted by S*, was detected in the synthetic seismograms computed for a P point source located in the proximity of the free surface. Strong dependence of the amplitude of the S* arrival on the depth of the source is seen in computed seismograms. It is shown that under favorable circumstances, i.e., when the source is less than one wavelength from the free surface, the S* arrival may be stronger than ordinary body waves at the same depth. This may be particularly important for studies of the seismic wave fields in oil exploration, where explosive sources are close to the surface. We show that the S* arrival, which features a linear polarization and propagates with the shear wave velocity, may be interpreted as a result of interaction between inhomogeneous plane waves in the integral representation of the P point source, and the free surface. Mathematically, the S* arrival corresponds to the saddle point contribution of the integral along the branch cut originating at the horizontal slowness p = α/β (α, β indicate P - and S-phase velocities, respectively). This branch cut must be considered when the saddle point approximation to the Weyl-Sommerfeld integral for a shallow P point source is used. Existence of another nongeometrical effect, namely the nonzero vertical component of the converted PS wave reflected from the free surface at normal incidence, is also shown. In our opinion, this arrival can be easily explained by higher order terms in the corresponding ray series. The prominence of both nongeometrical effects suggests they should be incorporated into any synthetic seismogram computations carried out for shallow explosive sources.