The cavity transfer matrix for the round trip of a light pulse in the optical resonator of the National Institute of Standards and Technology/Naval Research Laboratory free‐electron laser oscillator is derived. The cavity eigenmodes and the corresponding eigenvalues are obtained, using an expansion in Gaussian–Laguerre vacuum modes, by numerical diagonalization. The fractional power loss per eigenmode, caused by the finite sizes of the cavity mirrors and apertures, is determined. It is found that the losses are very small over the entire wavelength regime of operation.