We analyze the intensity characteristics of the output beams of the ring laser, in which only one mode is generated in each direction, within the neoclassical model by using the Maxwell-Bloch equation. Considering the Nd:YAG crystal as a gain medium, we investigate the stability and the modulation of the output beam intensity as the pumping rate, the relaxation or the decay rate, and the frequency detuning vary, upon taking into account the effect of the beam in one beam in one direction onto the beam in the other direction. In particular, we examine the variation of the output beam intensity and the stability condition through a computer simulation.