The shifts from gas-phase values of the vibrational and rotational states of H2 impurities substitutionally trapped in solid Ar are calcd. at zero temp. and at pressures 0 < P ? 438 kbar, using the recently developed H2-Ar potential of R. LeRoy and J. Carley (1980). At zero pressure, the calcd. matrix shift in Q1(0) is -21.5 cm-1, in good agreement with expt. Averaging the H2-Ar potential over the center of mass motion of the H2 and Ar atoms is an important correction. The shift in Q1(0) with pressure is very large and there is no indication of a turnover in this mode frequency at high pressures as is obsd. for pure solid H2 at P ~ 330 kbar. The shifts in the calcd. rotational and vibrational-rotational transitions are in less good agreement with expt. and the probable reason for this is discussed. [on SciFinder (R)]