Based on the examples of filled cellulous and the high filled polymer it was shown that mechanical behavior of polymeric materials depends substantially on the loading rate or the strain rate. The change of mechanical characteristics of filled cellulous with increasing of the strain rate in the interval from 7·10-6 to 700 s-1 is related to the change of dominating mechanisms of the resistance to deformation and fracture of material. The transition from viscous failure to brittle fracture is occurred at increasing of strain rate to several hundreds of inversed seconds. The criterion of the long-time resistance of polymeric materials was suggested. This criterion was based on the evaluation of the damage of the material. The damage increment was defined as the relation of the strain energy increment to value of the fracture energy at appropriate rate of deformation. The experimental verification of this criterion was carried out for the investigated materials as at tension so at complex stress state by the results of the tests with stepwise change of strain rate. The comparison of suggested criterion with well-known deformational criterion was carried out on the base of obtained experimental data It was shown that suggested criterion can be used for evaluation of time to fracture of polymeric materials at complex programs of loading with changing of strain rate in wide range.