The worm and gear are the key transmission components of the mechanism of azimuth angle of the disc type solar system, to make sure that the driving mechanism of azimuth angle have a safe and steady working condition, the contact stress of the worm and gear must be under the range of allowable stress under working conditions. Solid model of the worm and gear was established using the parameteric modeling method，the multi tooth contact finite element model of the worm and gear was established using the software ABAQUS. By the method of nonlinear contact analysis, the stress distribution of the worm and gear meshing momentary of contact tooth surface was studied. The results show that: the results error is only 1% between the results based on ABAQUS and result of Hertz contact stress theory, the worm and gear contact stress is less than the material allowable stress, but the root of the maxiumum stress value reached 258.3 MPa,and have obvious stress concentration, by increasing the fillet radius of the stress is reduced and the gear contact intensity increased. But the worm and gear is difficult to normal meshing and even can not work normally when fillet radius is larger than 5 mm.