In this paper with the further development of our previously published single exponential model, the new multiple exponential model describing the pressure dependence of acoustic longitudinal wave velocity is presented. Since with increasing pressure in the rock several relaxation mechanisms at the same time can cause the increasing propagation velocity, the new model can handle two or more physical mechanisms (e.g. the closure of pore volume or microcracks or friction on grain boundaries etc.). The previously applied linearized inversion procedure can trap in a local minimum, so during laboratory measured longitudinal velocity-pressure data processing a global optimization method was used to find the absolute minimum. Using the developed model equation as response equation in a Simulated Annealing algorithm the petrophysical parameters of the model can be determined. Inversion results proved that the calculated data using the new model and algorithm matched more accurate with measured data on a rock sample.