This paper presents a boundary element-free computational method for the fracture analysis of 2-D anisotropic bodies. The study starts from a derived traction boundary integral equation (BIE) in which the boundary conditions of both upper and lower crack surfaces are incorporated into and only the Cauchy singular kernal is involved. The boundary element-free method is achieved by combining this new BIE and the moving least-squares (MLS) approximation. The new BIE introduces two new variables: the displace density and The dislocation density. For each crack, the dislocation density is first expressed as the product of the characteristic term and unknown weight function, and the unknown weight function is approximated with the MLS approximation. The stress intensity factors (SIFs) can be calculated from the the weight function. The examples of the straight and circular-arc cracks are computed, and the convergence and efficiency are discussed.