The self‐focusing of relativistically intense laser light pulses is analyzed, where the pulse length is short enough that ion inertia prevents any significant motion of ions. Self‐focusing occurs as a result of an increase of the wave refractive index arising from two effects: the mass increase of electrons caused by their relativistic quiver velocity in the light wave, and the reduction of the electron density as a result of ponderomotive force expulsion of the electrons. The latter effect is significant even for rather small values of (P−P_L)/P_L, where P is the laser beam power and P_L is the critical power above which self‐focusing occurs. In fact, for (P−P_L)/P_L≳0.1 the effect is so strong that all electrons are expelled within a core radial region of the self‐focused laser light channel (this new phenomenon is called electron cavitation).