The single-row four-point-con tact ball-type slewing bearing is adopted in a type of anti-air gun. It plays an important role in the mechanical characteristics of the guru The influence of the bearing on the firing accuracy should be investigated carefully because of the complexity of the contact problem. This paper derives out the relationship between the deformations and the external loads in terms of the Hertzes theory. The firing bias of the gun caused by the horizontal rotating slewing bearing is estimated from a view point of statics and is shown to be a small quantity.