A specific Continuum Damage Mechanics model is developed in order to simulate the behavior and the burst of hyperbaric pressure vessels. This model uses the concept of fixed damage directions (related to the composite orthotropy axes), associated with the theory of tensorial functions representation. By the means of these tools, different damage modes (fibre breakage, matrix cracking, delamination,...) are taken into account as well as irreversible strains and the matrix viscosity. The procedure to identify the set of material parameters uses classical tension tests performed on the samples of different orientations in the framework of the project Osirhys IV led by the French Alternative Energies and Atomic Energy Commission (CEA). Copyright (C) 2015, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.