Abstract: Based on the progressive failure behaviour of rock mass.an elastic plus tic and limit state analyss method for the undergrouna rock strucure is developed.In the case of a circular tunnel,an idealized elastoplastic soften-ing and plastic dilation material model is set up;and aclosed form solution is presented for the axisymmetric plane strain case.It shows that there is ia limit failure state in the progress of the plastic zone around a tunnel.It hs the strain-softening and the plastic dilation behavinor of rock mass that save a heavy effect on the limit fairure state of a tunnel The solution of this paper is more practical and has a wider application cope shan the solutions which have been made.