Ultrasonic surface (Rayleigh) waves become dispersive when propagating on non-uniformly stressed media. In light of this, the Acoustoelastic effect on their propagation in deformed but initially isotropic materials has been investigated in the past, in order to determine the surface stress and gradients of stress with depth. An energy perturbation approach considerably reduces the complexity in the treatment of the Acoustoelastic effect and inversion of the perturbation relation offers an advantageous route to obtaining the stress gradients. This paper presents a new mechanism for effecting this inversion, which tries to overcome the effects of the ill-posed nature of the problem. Preliminary simulation results for commonly occurring stress profiles are presented.