At present

the tunnels and big underground space were excavated in the fractured rock; their stability are controlled by crack growth condition and distance from crack and tunnel and underground space. By applying the new boundary integral equation (BIE) for two-dimensional elastic bodies containing cracks and holes to couple the element-free Galerkin method

a new boundary element-free solution for calculating the interaction between cracks and holes is presented. The basic unknown in the new boundary integral equation is a complex boundary function

which is a linear combination of the boundary traction and boundary displacement density. The present BIE formulation can be related directly to Muskhelishvili’s formalism. The constructed methods of the element-free try functions are introduced into the new boundary integral equation to develop the new boundary element-free solution. At last

the validity and accuracy of the presented method are illustrated by the elastic mechanics problem containing cracks and tunnel from that the method results agree well with those obtained from the analytical solution.