In reverberation modeling for rough bottom, a surface integration is conducted along elemental scattering areas with repetitive uses of propagation and scattering strength models and a summation of scattered signals from the scattering areas provides a synthetic reverberation signal in time domain. In particular, when roughness is on a flat or sloping bottom, numerical integration schemes including quadrature by parts can be used with elemental scattering areas, which are small enough to obtain a converged reverberation signal. However, this standard approach is unavailable for a bottom having irregular geometry since the bottom cannot be divided into small element scattering areas. To acquire a stable reverberation signal by the irregular bottom, we derive an analytic integration of scattered signal for polygon facet by using Stokes’ theorem while approximating the bottom with combination of polygon facets. In this approach, a delay difference in an elemental scattering area is considered whereas a representative delay is used for the elemental scattering area in the standard approach. Results from two different reverberation models are compared and the scheme using analytic integration shows a converged reverberation signal even with large elemental scattering areas.