Bunch radiation in periodical waveguides was mainly analyzed for situations when wavelengths are comparable to the structure period (Smith-Purcell emission). However, it is also interesting to study long wave radiation with wavelengths which are much greater than the structure period. In this paper, the electromagnetic field is analyzed using the method of equivalent boundary conditions. According to this approach, the exact boundary conditions on the complex periodic surface are replaced with certain equivalent conditions which must be fulfilled on the smooth surface. We consider a vacuum circular waveguide with a corrugated conductive wall (corrugation has rectangular form). The charge moves along the waveguide axis. The period and the depth of corrugation are much less than the waveguide radius and wavelengths under consideration. Expressions for the full field components and the wave field components are obtained. It is established that radiation consists of the only one TM waveguide mode which is excited if the charge velocity is more than certain limit value. Dependencies of the frequency and amplitude of the mode on the charge velocity and parameters of corrugation are analyzed. It is demonstrated that typical amplitude of waveguide mode from the ultra relativistic bunch has the same order as one in the ordinary regular waveguides with dielectric filling. In order to verify the method applied in this work we have simulated the electromagnetic field using the CST Particle Studio. For this purpose, we have considered the charged particle bunch with negligible thickness and Gaussian longitudinal distribution. It has been shown that the coincidence between theoretical and simulated results is good. This fact confirms that the theory based on the equivalent boundary conditions adequately describe the radiation process in the situation under consideration. The obtained results can be useful for development of methods of the electromagnetic radiation generation and technique of the wakefield acceleration of charged particles.