Abstract: For soil, rock and concrete, failure surface is irregular in ordinary stress space because of the influence of hydraulic pressure and Lode’s angle of stress to their strength. Based on Lade’s criterion and exponential failure function in coordinate p-q, a new transformed stress tensor is proposed in this paper. With this transformed stress tensor, the irregular failure surface in the ordinary stress space can be transformed into a cone in the transformed stress space without adding any new parameters. Analyzing the test data in the unified transformed stress framework, the complex stress strain relationship may be transformed into single and simple ones.