The density evolution of a semi-crystalline Poly(lactic acid) under ultra/high pressure histories in the region of alpha relaxation has been studied. It was found that the degree of crystallinity does not change in the temperature and pressure ranges under concern and consequently it is assumed that the volume relaxation kinetics involves only the amorphous part of the polymer. The scaling law for relaxation times, recently proposed by Casalini and Roland, has been utilized in the framework of KAHR (Kovacs Aklonis Hutchinson and Ramos) phenomenological theory in order to model the volume relaxation behavior. With this approach the model contains only two fitting parameters, (namely the relaxation time in the reference state, tau(g), and the fractional exponent, beta, that describes the dispersion of the alpha relaxation) instead of the five parameters of the classical KAHR theory. The model predicts accurately both the density evolution of the PLA during the sterilization and Pasteurization treatments simulated in a pressure dilatometer and the density changes occurring in the PLA films utilized as packaging material in the HP industrial processes. (C) 2011 Elsevier Ltd. All rights reserved.