In this thesis, we propose an analytical method that provides quick and accurate surface-wave solutions for solving coaxial-cavity gyrotron with a longitudinally corrugated insert which has dielectric-filled grooves. Using ACBC- the asymptotic corrugated boundary condition, it is quite simple and briefly to obtain not only the dispersion relation between the frequency and wavenumber but the field distribution from the solution of the characteristic matrix. Results of dispersion and field distributions generated by ACBC analysis are validated with CST which is a commercial full-wave simulation software. Results of conductor losses with various parameter studies are also reported.