An investigation of the growth of a radially symmetrical ripple, superimposed on a Gaussian laser beam in a plasma is presented. Based on WKB and paraxial ray approximation the phenomenon of relativistic self-focusing (RSF) is analytically investigated. The differential equation for beamwidth parameter of rippled laser beam is evaluated. The ripple gets focused when the initial power of the ripple is greater than the critical power for focusing. The focusing is found to be considerably affected by the power of the main beam and the phase angle between the electric vectors of the main beam and the ripple. At higher intensities the saturation effects of nonlinearity become predominant, making the nonlinear refractive index in the paraxial region have slower radial dependence, and thus the ripple extract relatively less energy from its neighborhood. The case of magnetized plasmas is also preliminarily discussed.