The PY, HNC and VM integral equation theories are used to study the structure and thermodynamics of the hard prolate spherocylinder fluid. Results for the spherical harmonic coefficients of the pair distribution function and for the compressibility factor are compared with computer simulation data, including new results reported in this work, for length-to-breadth ratios up to γ = 6. For γ = 2 the VM structural results agree quantitatively with those of the simulations. For γ = 3, the results are mixed. For γ = 6 the HNC results are the best. The PY results are the worst at any value of γ considered. The VM compressibility factors agree excellently with those of the simulations for all length-to-breadth ratios, while the HNC values are too high and the PY values too low. Finally, we propose a geometrical argument explaining the accuracy of the HNC for very elongated molecules.