  An analytical solution of the Helmholtz equation for electromagnetic field
distribution in a resonant cavity with elliptic cross-section is found. We
compare the frequencies of the eigenmodes with numerical and experimental
values for a metallic cavity and find an excellent matching. We focus our
analysis on the microwave frequency region, and show how the ellipticity of the
cavity (ratio of the minor and major axes length $b/a$) influences several mode
frequencies and also the $Q$-factor of the cavity. By doing so, we demonstrate
how the elliptic geometry splits the degeneracy of certain modes of the
circular cylindric cavity.
