This paper presents an investigation into the behavior of a laser beam of finite diameter in plasma with respect to forces and optical properties, which lead to self-focusing of the beam. The transient setting of ponderomotive nonlinearity in a collisionless plasma has been studied, and consequently the self-focusing of the pulse, and the focusing of the plasma wave occurs. The description of a self-focusing mechanism of laser radiation in the plasma due to nonlinear forces acting on the plasma in the lateral direction, relative to the laser has been investigated in the nonrelativistic regime. The behavior of the laser beams in plasma, which is the domain of self-focusing at high or moderate intensity, is dominated by the nonlinear force. The investigation of self-focusing processes of laser beams in plasma results from the relativistic mass and energy dependency of the refractive index at high laser intensities. Here, the relativistic effects are considered to evaluate the relativistic self-focusing lengths for the Nd glass radiation, at different plasma densities of various laser intensities. A numerical program in c++ that incorporates both the ponderomotive force in self-focusing mechanism and relativistic effects has been developed to explore in depth self-focusing over a wide range of parameters.