In view of the optimal theory and the concept of approximate feasibility and a series of common difference criterion functions, and based on the nonlinear accelerant simplex method, a nonlinear displacement stochastic back analysis model of rock mass named flexible tolerance method is developed. The method is wide in adaptability, quick in convergence and high in efficiency. Considering the stochastic properties of measured deformations and material parameters the object function of nonlinear displacement stochastic back analysis is applied. Elastoplastic?cracking model is employed in rock mass, and nonlinear iteration uses increment changeable Kp method. The back analyzed result from an  engineering example indicates that both the frequency of transfering FEM program and the time -  expending of operating Computer obtained by the flexible tolorance method are less than those got with the complex method, and the difference of the two calculated results is very small. It enough verifies the effectiveness and feasibility of the method.