We present the mathematical formulation and numerical results for the resonance characteristics of the TMmp modes in a coaxial cavity with a longitudinally corrugated insert. Based on the spatial harmonics method, the eigenvalues of the transverse plane are calculated, and then, the Vlasov approximation is used to calculate the resonance frequency, diffractive quality factor, and longitudinal field profile of every mode. The numerical results are presented and compared with those found in the literature.