Hydrogen bonds can significantly influence the properties of molecular glass formers, particularly with respect to their elasticity. We present an ultrasonic study of the elastic properties of liquid and glassy glycerol (a substance with hydrogen bonding) under pressure, comparing to the similar results obtained for propylene carbonate (a substance without hydrogen bonding). Pressure dependences of the isothermal bulk modulus are almost linear for both liquids with relatively similar slopes. The values of the pressure derivative of the bulk modulus (7.8 for glycerol and 8.6 for PC) indicate that the pair intermolecular interaction in both liquids is close to that in the Lennard-Jones liquid. This also firmly means that the volume–temperature scaling in glycerol with volume exponent 1.4–1.8 in contrast to PC does not correlate with the effective repulsive part of the pair potential. Pressure dependences of elastic moduli for glassy PC and glycerol are nonlinear and demonstrate similar trends with pressure. The ratio of the elastic moduli of glassy glycerol to the appropriate values of PC is approximately 2–2.5 at atmospheric pressure, as in liquid states. The Poisson's ratio of glycerol is less than that of PC and closer to 0.25 which indicates a relatively higher role of central forces. The observed differences in elastic behavior between liquid or glassy glycerol and PC are discussed in terms of the role of strong hydrogen bonding in glycerol.