This paper presents an analysis of relativistic self-focusing of a Gaussian laser beam incident normally on a plane interface of a linear medium and a nonlinear, nonabsorbing plasma with an intensity dependent dielectric constant. Considering the nonlinearity to arise from the relativistic variation of mass and the Lorentz force on electrons. Following Wentzel–Kramers–Brillouin (WKB) and paraxial ray approximation the phenomenon of relativistic self-focusing of the transmitted laser radiation has been analyzed for the arbitrary magnitude of nonlinearity. Change in the intensity distribution along the wavefront of the Gaussian beam, due to refraction at the interface has also been taken into account. The variation of beamwidth parameter with distance of propagation, self trapping condition and critical power has been evaluated. Numerical estimates for typical parameters of laser plasma interaction process indicate the refraction at the interface to have a significant effect on self-focusing.