Accidents of water leakage and bursting due to deterioration of water pipes cause water outages and economic losses in the surrounding areas. We are conducting research to develop measurement and diagnostic methods for buried water pipes. The graphitic corrosion of water pipes in a buried environment causes a reduction in pipe thickness which leads to strength problems. For this reason, methods for detecting pipe thickness are necessary for evaluating pipe deterioration, however, there is no effective way to analyze pipe thickness today because it cannot be visually observed in a buried environment. In this study, we focused on the shift in eigenfrequencies of in-plane bending vibration of rings due to deterioration. At first, we performed an experimental modal analysis by using a water pipe network which is used in a practical water utility. In addition, we conducted a theoretical analysis based on a model of a two-dimensional ring with coupled incidental attachment. As a result, in-plane bending vibration was observed in the water pipe of actual size. Furthermore, in-plane bending vibration was observed when excited through fire hydrants and it is also observed in pipes that are different material and diameters.