At the ultra-high frequencies (UHF) common to portable radios, a mine tunnel is often modeled as a hollow dielectric waveguide. The roughness condition of the tunnel walls has an influence on radio propagation and therefore should be taken into account when accurate power predictions are required. In this paper, we derive a general analytical formula for modeling the influence of the wall roughness. The formula can model practical tunnels formed by four dielectric walls, with each having an independent roughness condition. It is found that different modes are attenuated by the same wall roughness in a different way, with higher order modes being significantly more attenuated compared to the dominant mode. The derivation and findings are verified by numerical results based on both ray tracing and modal methods.