Time-dependent failure of PMMA and polyethylene are characterized within the framework of a cumulative damage model for failure. It is found that the mean failure times in constant rate of stress experiments can be successfully predicted from the model using a time to fail function determined from constant stress experiments. For zero-tension sinusoidal fatigue tests, differences of up to an order of magnitude are observed between predicted and experimental failure times. PMMA and polyethylene data deviate from the predictions in different ways. In PMMA, the distribution of failure times in constant stress tests is moderately broad, as measured by the coefficient of variation, and symmetric about the mean, while in the fatigue tests the distribution is considerably broader, has a high positive skewness and shows evidence of being bimodal. For polyethylene, the distribution changes from being moderately broad and positively skewed in constant stress tests to a moderately broad, symmetric distribution in the fatigue tests. The model also predicts the total lifetime in sinusoidal fatigue tests to be independent of test frequency. Experimental results show that the lifetime of PMMA decreases with increasing frequency, although less rapidly than if the fatigue process were cycle dependent. The lifetime of polyethylene increases with increasing test frequency.