Inelastic scattering of a low-energy atomic helium beam (HAS) by a physisorbed monolayer is treated in the one-phonon approximation using a time-dependent wave,packet formulation. The calculations show that modes with shear horizontal polarization can be excited near high symmetry azimuths of the monolayer, in agreement with recent experiments. The parameters of the calculations are chosen to match the conditions of HAS experiments for triangular incommensurate monolayer solids of xenon, krypton, and argon adsorbed on the (111) face of platinum, and the results show many of the systematic experimental trends for relative excitation probability of the shear horizontal and longitudinal acoustic phonon branches. The inelastic scattering at beam energies near 8 meV is exceedingly sensitive to small misalignment between the scattering plane and the high symmetry directions of the monolayer solid. The diffraction and inelastic processes arise from a strong coupling of the incident atom to the target and the calculated results show large departures from expectations based on analogies to inelastic thermal neutron scattering.