Comparing with general optical fiber sensors performing localized measurement, the distributed optical fiber sensors measure along the length of an optical fiber and thus they have a large measuring range. This implies that the distributed optical fiber sensors are very effective in the health monitoring of large structures. The Brillouin scattering is one of the inelastic scatterings in optical fibers, and it can be used in the measurement of strain and temperature with the Brillouin frequency shift. The surface- mounting with epoxy is generally used in the application of optical fiber sensors to monitoring structures. This is also used in the integrity monitoring of structures with the Brillouin-scattering distributed optical fiber sensors. In this research, the Brillouin-scattering distributed optical fiber sensors, which are mounted on the surface of a structure with epoxy, was evaluated with the finite element method. From the analysis results of the strain transfer through the structure, epoxy adhesive, optical fiber coating, cladding and core, the strain transfer rate was calculated. By using the strain distribution, the influence of the epoxy free-end was also studied.