The elastic differential cross-section forē-Na scattering in the presence of non-resonant laser field is studied for the exchange ofℓ=0, 1, 2 photons. The undressed contribution is evaluated within the framework of the eikonal Born series approximation and the effect of exchange is taken into account via the Ochkur approximation. The sodium atom has been treated in the frozen core approximation with special attention to the effect of the dressing of the target by the laser field. The ‘dressing’ of the target leads to quite an increase in the cross-section over the ‘undressed’ value near the forward direction for the exchange of one or two photons.