Abstract: The Percus-Yevick (PY) and hypernetted-chain (HNC) integral equations have been solved to calculate the angular pair-correlation functions (PCFs) of the isotropic phase for a fluid of hard ellipsoids of revolution represented by a Gaussian overlap model. The methods used involve an expansion of angle-dependent functions appearing in the integral equations in terms of spherical harmonics and the harmonic coefficients are obtained by an iterative algorithm. All the terms of harmonic coefficients which involve l indices up to $\le$ 6 have been considered. The numerical accuracy of the results depends on the number of spherical harmonic coefficients considered for each orientation-dependent function. Ellipsoids with length-to-width ratios (x_0) of 2.0 and 3.0 are considered and the harmonic coefficients are compared with the molecular-dynamics results for prolate ellipsoids. It has been observed that both the PY and HNC theories are in reasonable agreement with the computer simulation results. The pressure obtained from the virial and compressibility routes of these fluids have also been compared with the computer simulation results which show that these integral equations are thermodynamically inconsistent. These results have been used in the density-functional theory to locate the freezing transitions of these fluids. We find that the density-functional theory is good to study the freezing transitions in such fluids.