We present results of lattice dynamics calculations of Poisson's ratio (PR) for solid hydrogen and rare gas solids (He, Ne, Ar, Kr and Xe) under pressure. Using two complementary approaches-the semi-empirical many-body calculations and the first-principle density-functional theory calculations we found three different types of pressure dependencies of PR. While for solid helium PR monotonically decreases with rising pressure, for Ar, Kr, and Xe it monotonically increases with pressure. For solid hydrogen and Ne the pressure dependencies of PR are nonmonotonic displaying rather deep minimums. The role of the intermolecular potentials in this diversity of patterns is discussed. (C) 2015 AIP Publishing LLC.