The second virial coefficient of 2-center Lennard-Jones molecules which have an embedded point quadrupole has been determined ia numerical integration. A number of models with different reduced bond lengths and quadrupole moments have been considered. For each model the second virial coefficient has been determined for a range of temperatures. It is shown that the presence of the quadrupole moment significantly raises the Boyle temperature and, for a certain temperature, reduces the value of the second virial coefficient with respect to the non-polar model. Empirical fits for B₂ are given which reproduce the generated data. It is also shown that the inclusion of the quadrupole considerably improves the description of B₂ for real substances which have a significant quadrupole moment, as is the case for CO₂ . The inclusion of the quadrupole is also required for understanding the cross virial coefficient between a spherical and a quadrupolar molecule, for example the interaction between Xe and CO₂.