In the present investigation, the analytical investigation of nonlinear propagation of intense electromagnetic waves through under dense inhomogeneous plasmas, taking into account the relativistic nonlinearity, is presented. The relativistic ponderomotive force is shown to have a major effect on nonlinear dynamics of the propagation of intense electromagnetic waves. It is seen that a plane wave of uniform intensity becomes unstable and gets filamented in the presence of transverse density fluctuation in the plasma. For a linear density profile the amplitude of the filament varies with z as an Airy’s function. The growth rate increases with transverse wave vector of the perturbation. The characteristic growth length decreases with the size of perturbation and the ratio of expansion velocity to sound velocity. It increases with the angle laser k vector makes with the density gradient.