The dispersion curves of all three phonon modes, the shear horizontal (SH), longitudinal (LA), and perpendicular (S) vibrations of the two-dimensional monolayer inert gas solids of xenon, krypton, and argon on Pt(111) have been measured by inelastic helium atom scattering (HAS). Previous HAS measurements of xenon on other substrates revealed, in addition to the S mode, only a single dispersive mode which deviated strongly from the expected behavior of the LA branch, to which it had been assigned. The new measurements now identify this mode as the SH mode and all three modes are in excellent agreement with calculations based on the inert gas pair potentials determined from gas and bulk solid data. Possible mechanisms for the excitation of the SH branch, which should couple only very weakly to HAS on the basis of symmetry considerations, are discussed. (C) 2000 American Institute of Physics. [S0021-9606(00)70104-8].