The hypernetted-chain (HNC) and Percus–Yevick (PY) approximations are solved numerically for isotropic fluids of hard spherocylinders with length-to-breadth ratios ranging from 2 to 6. The theoretical results are compared with the available Monte Carlo data for the equation of state and the pair correlation function. The HNC theory was found to predict the existence of a nematic phase at densities in reasonable agreement with recent computer simulations.