The equilibrium properties of isotropic fluids composed of hard ellipsoids of revolution represented by a Gaussian overlap model are studied using the integral equation theories. The Percus-Yevick and the hypernetted-chain integral equations have been devised for calculating the angular pair-correlation function for fluids of hard ellipsoids of a revolution. This model is computationally simple and shears some similarities with the widely used hard ellipsoids. 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. We have considered all the terms of harmonic coefficients which involve l indices up to less than or equal to 6. The numerical accuracy of the results depends on the number of spherical harmonic coefficients considered for each orientation-dependent functions. Ellipsoids with length-to-width ratios of 2.0 and 3.0 are considered and the harmonic coefficients are compared with the molecular-dynamics results for prolate ellipsoids. We find that both the Percus-Yevick and hypernetted-chain 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 shows that these integral equations are thermodynamically inconsistent.