Abstract: Motion equations of electrons and the evolution of optical field in FEL oscillators written in 2-D cylinder coordinates have been solved by numerical simulations . In no-source region (outside Wiggler), the no-source, paraxial wave equation obtained by non-self-consistent method has been deduced; and the correspondent code R-2D has been programmed. It is found that has been the agreement between the results of 2-D numerical simulation by R-2D and those of Gaussian beam approximation is quite satisfactory when a source is considered. Under the same condition of computation, the simulation results obtained by R-2D is rather approximate to those of FELEX at LANL. After the primary simulation and analysis, we think that the experimental data published by LANL is physically rational, and its simulation results is credible. At last, some simulation results of Beijing FEL project are presented.