In this contribution, two new criteria and related methodologies for the prediction of the long-term (creep rupture) behavior of single layer and multilayer plastics pipes under hydrostatic pressure are presented. One of these is the ultimate strain extrapolation method (USEM) and the other is called the distortion energy extrapolation method (DEEM). The strain concept is based on the use of the failure strain criteria instead of the normally employed stress concept. A related long-term extrapolation methodology is presented that employs the ultimate strain instead of the rupture stress. The strain energy concept is based on the use of the distortion energy corresponding to the failure stress. For both of these two criteria, related extrapolation methodologies are introduced. An example is presented that compares the classical standard extrapolation method (SEM) with the ultimate strain and the energy methods. For correlation of various models, an example of a PVC-U pipe under internal hydrostatic pressure at T=20 °C was studied. The three models employed were the stress-based, the strain-based, and the energy-based regression analyses. Direct regression analysis was performed for all three failure criteria. However, for comparison, the modified version of the SEM was also used. In all cases, a complete match between the independent model and the modified SEM analysis was obtained. A backward calculation of failure stress from the long-term failure distortion energy gave a 50-year failure stress equal to 18.59 MPa. This value was lower than the stress-based extrapolation (25.37 MPa) and higher than the strain-based extrapolation. The proposed USEM is suitable for materials which fail due to the ultimate strain state and not necessarily due to the maximum stresses. Thus, the proposed strain extrapolation criteria may prove to be especially suitable for brittle and fiber reinforced materials. The strain-based extrapolation can be used in connection with rupture data in internal hydrostatic tests or creep rupture of pipe samples under other loading conditions. The DEEM, on the other hand, is believed to be applicable to a broad range of material types. The proposed methodologies can be used as a new guideline for prediction of the service life of single layer brittle thermoplastics pipes, glass fiber reinforced laminate pipes, and multilayer plastics pipes with fiber reinforced layers.