Solid-fluid equilibrium for the quadrupolar hard dumbbell model has been determined by Monte Carlo simulation for several values of the quadrupole moment and molecular elongation. Several solid structures have been studied including α-N2, a fee plastic crystal, based centered monoclinic structure providing closest packing for hard dumbbells and two orthorhombic structures. For low elongations, hard dumbbells freeze into a plastic crystal phase when the quadrupole moment is low and into the α-N2 structure when it is large. More elongated dumbbells freeze into a close-packed structure for low quadrupole moment, into an orthorhombic structure for moderate quadrupole moment and into the α-N2 structure for large quadrupole moment. For any elongation and quadrupole moment the stable phase at very high pressures is one of the close-packed structures. The quadrupolar hard dumbbell model gives a qualitatively correct description of trends in the solid-fluid equilibrium for several systems including N2, the halogens, CO2, and acetylene. © 1995 American Institute of Physics.