Abstract: High-resolution X-ray photographing needs to focus intense relativistic electron beams of several thousand amperes on bremsstrahlung converter target, thereon forming a small and stable spot. In the ideal case,electron beams cn be focused to a poing. However, due to the influcence of such factrs as the space charge effect, the beam emittance, the spherical aberration of the lens, and the chromatic aberration, the minimization of the spot size of electron beams is limited. Furthermore, the corkscrew oscillaton of the beam centroid not only leads to the increase of the spot size but also to the distortion of the spot shape. The effects of solenoidal field on the spot size of intense relativistic electronic beams are analyzed and the minimal spot sizes limited by various factors are given. Th