The endochronic theory with kernels is likely to be useful for the FEM analysis of concrete structures under multiaxial stresses. This paper describes the numerical procedure for the application of this theory to the structural analysis. This procedure contains the following items. (1) If the major principal tension stress is greater than the tensile capacity of the concrete,cracking will occur along a plane normal to the principal stress direction. (2) In each increment, an iterative method is required until convergence is obtained. Analysis of the cross section of a fill dam gallery was conducted by using this procedure, and the behaviors of the gallery were discussed comparing with the elastic analysis.