We propose a technique for determining elastic properties of a medium by the AVO-inversion for postcritical reflections. The inverse problem is solved by Nelder-Mid optimization method. Numerical experiments were used for testing the accuracy and stability of the algorithm for different offset ranges and initial models. It is shown that the velocity estimations can be obtained with the error <1% for all the offset ranges considered, if noise is absent. In the presence of noise the accuracy of the S-wave velocity estimation is lower at the precritical offsets. Using the nearcritical and postcritical offsets we obtain the errors <1% in the P-wave velocity and <6% in the S-wave velocity , when signal/noise ratio is >5