The viscoelastic properties of the resins used in carbon fiber composite pressure vessels introduce time effects which allow damage processes to develop during use under load. A detailed understanding of these processes has been achieved through both experimental and theoretical studies on flat unidirectional specimens and with comparisons with the behavior of pressure vessels. Under steady pressures, the relaxation of the resin in the vicinity of earlier fiber breaks gradually increases the sustained stress in neighboring intact fibers and some eventually break. The rate of fiber failure has been modeled based only on physical criteria and shown to accurately predict fiber failure leading to composite failure, as seen in earlier studies. Under monotonic loading, failure is seen to be initiated when the earlier random nature of breaks changes so as to produce clusters of fiber breaks. Under steady loading, at loads less than that producing monotonic failure, greater damage can be sustained without immediately inducing composite failure. However, if the load level is high enough failure does eventually occur. It has been shown, however, that below a certain load level the probability of failure reduces asymptotically to zero. This allows a minimum safety factor to be quantitatively determined taking into account the intrinsic nature of the composite although other factors such as accidental damage or manufacturing variations need to be assessed before such a factor can be proposed as standards for pressure vessels.