We present molecular dynamics simulations of the homogeneous (mechanical) melting transition of a bcc metal, vanadium. We study both the nominally perfect crystal as well as one that includes point defects. According to the Born criterion, a solid cannot be expanded above a critical volume, at which a 'rigidity catastrophe' occurs. This catastrophe is caused by the vanishing of the elastic shear modulus. We found that this critical volume is independent of the route by which it is reached whether by heating the crystal, or by adding interstitials at a constant temperature which expand the lattice. Overall, these results are similar to what was found previously for an fcc metal, copper. The simulations establish a phase diagram of the mechanical melting temperature as a function of the concentration of interstitials. Our results show that the Born model of melting applies to bcc metals in both the nominally perfect state and in the case where point defects are present.