The Weibull stress (Beremin, 1983) relates the local first principal stress and plastically strained volume to the probability of fracture. It requires two constants (m, σu) as input, which are generally regarded as material parameters. As the Beremin approach is used in the background to structural analysis rules, the Beremin parameters are now being used in other situations, including engineering analysis. However, the currently accepted way to find the Beremin constants requires twenty tests, which is considered to be unacceptably expensive for industrial application. Less expensive ways of finding the Beremin parameters have been published in the literature, but they have never been compared to the de facto standard. In this paper, the Beremin parameters were found by the de facto standard method and two other ways, and a comparison is made. It was found that the Beremin parameters can be estimated with reasonable accuracy with a method that uses on just two sets (six specimens) of fracture specimens by careful application of the method of Andrieu (2012). Also, a proposal is made for another method which is based only on the Master Curve temperature T0.