Nowadays because of the shortage in the fossil fuel resources and energy crisis, use of substitute fuels in the automobiles must be considered. One of this new fuels for the automobiles is natural gas that for the low level of energy in the unite of volume, it must be stored in the high pressures that has economical advantages. For this reason, we use of pressure vessels with high pressure endurance. These pressure vessels are generally in four types: type I – full steel pressure vessels, type II – steel pressure vessels with composite wrapped in cylindrical part of the vessels, type III – composite pressure vessels with metallic steal linear and type IV - composite pressure vessels with high density polyethylene (HDPE) linear. Because of the light weight and the safety in bursting than metallic pressure vessels, the use of composite pressure vessels in automobile industry is too important; so design and modeling of these pressure vessels (type IV) are the goal of this research. For this purpose, we used of finite element analysis in ABAQUS software. Geometrical parameters based on one of the industrial ways of production i.e. planar or polar filament winding, have extracted and have been used in the model and also design parameters are define from standards. For analysis of these pressure vessels we need a knowledge and usage of a proper failure criteria that this works have been done in this thesis. It is good to mentioned that the failure criteria for composite material are large in number that knowledge, understanding, sorting and scoring of them are considered and also we mentioned to the word wide failure exercise (WWFE) activities in this issue. Also, degradation equations (mainly Puck and Tsai-Wu failure criteria and degradation models) have been used in USDFLD subroutine that leads to a nonlinear solution. This nonlinear solution gives us a better behavior of composite material based on experimental parameters and consequently we have a pressure vessel with minimum weight to volume fraction with use of proper failure criteria and finite element method. Key words Composite material, failure criteria, CNG, FEA, ABAQUS, subroutine, USDFLD