The evolution of the two-dimensional radiation pulse in the free electron laser (FEL) oscillator is analyzed in association with electron pulses with arbitrary radial and axial profiles. In the FEL interaction region, the transverse variation of the wave equation is evaluated analytically, while the axial and the temporal variations are evaluated numerically. In free space, the radiation pulse is decomposed into Gaussian resonator modes and propagated analytically. Numerical results in the small electron beam radius limit, i.e., the radius of the electron beam much smaller than the minimum waist of the resonator mode, are presented.