Cylindrical resonant cavities with micro-structured cavity walls are proposed. The cavity was surrounded by a circular dielectric boundary with periodic rectangular corrugation. The corrugation is a kind of a curved resonant grating and functions as a highly reflective mirror for a diverging cylindrical wave inside the cavity. Basic characteristics of the resonant grating mirror and the cavity were investigated through numerical simulation. The results obtained indicate that such a structure can be useful for the construction of large area single-mode resonant cavities.