Conventional methods for obtaining failure envelopes require testing multiple samples, a luxury not enjoyed when dealing with core recovered from boreholes. Consequently, a multistage test performed on a single plug is attractive not only because it requires a single sample but it is both less expensive and requires less time. It has another major advantage in minimizing sample heterogeneity. Previous studies using multistage triaxial tests indicate that they can be an efficient approach to determining mechanical properties. However, critical to the recovery of meaningful data is the definition of the stress cycle termination point. We propose a new approach to defining the termination point. In this study, plugs from a common block of Berea sandstone were tested using both conventional and multistage triaxial testing methods. In our multistage tests we evaluated the inflection point of the volumetric strain curve i.e., when the derivative of the volumetric strain is equal to zero, as a termination point.The values of Young's modulus, E and Poisson's ratio, v, and the failure envelope characteristics show better agreement with those derived from single-stage conventional tests when the new termination criterion is used.