Underground environments are preferred for the construction of important infrastructures to overcome social problems, such as the tunnel or disposal of radioactive waste at deep depth. Concrete is primarily used as a structural material owing to its high strength and cost efficiency. To utilize these structures safely in the long term, the permeability of the concrete should be monitored. If the permeability is increased due to crack generation in a concrete medium, groundwater can flow into the underground structure. However, permeability monitoring is challenging at depths of 500 m–1 km under high-temperature, high-pressure, and limited space conditions. In this study, a theoretical model was developed to predict the permeability of concrete using compressive elastic waves. To derive the relationship between the permeability and elastic wave characteristics, Biot’s model, which can associate the characteristics of P-waves with the properties of porous media, was applied. The P-wave velocity and attenuation were investigated according to the permeability of the concrete based on Biot’s model. Subsequently, the concrete specimens were prepared to measure the permeability, P-wave velocity, and attenuation, and the permeability results from the experiment were compared to those obtained from the model for validation. Biot’s model is expected to be useful for permeability monitoring based on the characteristics of the elastic waves in underground structures.