In an underdense plasma a large‐amplitude plasma oscillation may be produced by the beating of two electromagnetic waves with a frequency difference approximately equal to the plasma frequency. In the spatially one‐dimensional, cold, and collisionless plasma the large‐amplitude plasma oscillation is limited by the nonlinearity caused by relativistic effects. In this paper a simple nonlinear equation, resembling the original equation of Rosenbluth and Liu [Phys. Rev. Lett.29, 701 (1972)], is derived in the weak beat power limit from the fully relativistic fluid model proposed by Sprangle, Sudan, and Tang [Appl. Phys. Lett.45, 375 (1984); Phys. Fluids28, 1974 (1985)]. This equation also contains the effects of the relativistic transverse motion. Its analytical solution, describing the plasma oscillation dynamics, is given in a closed form by using Jacobian elliptic functions. The analytical computations are compared with numerical computations. Finally the fully relativistic equation, describing free plasma oscillations, is studied analytically.