We analyze the wave field of a charged particle bunch moving in a circular waveguide consisting of two parts: the first one has a corrugated wall and the other one has a smooth wall. It is assumed that the period and the depth of the corrugation are much less than the waveguide radius and wavelengths under consideration. The influence of corrugation on the electromagnetic field is analyzed using the method of equivalent boundary conditions (EBC). The cases of the bunch moving in both directions inside of such a waveguide are considered. We obtain analytical expressions for the main part of the field having discrete spectrum. Figures of a typical mode distribution of radiation are presented. We also perform numerical simulations in software package CST Particle Studio. Comparison of analytical and numerical results confirms the validity of the EBC method.