The volume fraction effect of carbon fiber in an epoxy matrix in the vicinity of the notch on the traction and torsion behavior were studied. This volume fraction which increases with the reduction of the thickness is a parameter which proved effective on the capacity of resistance. The calculations are done with the numerical code ABAQUS 2009 [1]. using the model Hashin with shell elements of the structure. The objective of this study is to simulate the damage of stratified composite materials, the effect of several parameters such as the stacking sequence and the increase of the thickness of the folds having the same orientation of the structure, were evaluated and presented by load-displacement curves. The results obtained from the study illustrate the variation of damage as a function of these effects which act simultaneously and which also show that these modifications have a higher absorption capacity than that without modifications.