The detection of micro-cracks or degradation of strength of materials at the early stage of fracture is of increasing importance in power plants and aviation industry. A methodology of detecting micro-cracks or degradation of material using quasi matrix pencil method is presented in this paper. The damage is represented by small local elastic modulus reduction. Response of axisymmetric longitudinal guided waves to the presence of modulus reduction is studied using the Finite Element Method (FEM). Only the axisymmetric damage is considered here. By using this method to calculate the dispersion relation of excited wave mode, the small modulus reduction can be detected. Using the velocity of excited guided wave and the time point at which the calculated dispersion curve changing, the damage can be located. So this method can be used to find micro-cracks or material degradation at the early stage of fracture.