In this paper we have studied the problem of self‐focusing of a Gaussian laser beam in a collisionless magnetoplasma when the direction of wave propagation is at right angles to the magnetic field. The nonlinearity arises through the ponderomotive force and subsequent redistribution of plasma along the magnetic field. It is seen that as the magnetic field increases the extent of self‐focusing increases. The isointensity surfaces of a three‐dimensional beam are elliptical. In the case of a plane‐uniform laser beam it is seen that it is unstable for small‐scale fluctuations, and the growth rate of instability increases very rapidly with magnetic field.