The contact stress of flexible joint is an important factor affecting the safety of ultra-short-radius drilling tools. However, calculating the contact stress accurately is difficult, because the method for solving the multibody collision of the flexible joint is complex. A novel analytical method for the contact stress of ball cage flexible joint is presented in this study. The method was used to establish the relationship between the parameters and contact stress of the flexible joint during the drilling process. The contact stress analytical models of the ball head, ball key, and ball seat were established based on Hertz contact theory, and the finite element method was used to analyse the variations of contact stress under the weight of bit and torque. The influences of borehole curvature and deflection angle on contact stress were discussed for parameter optimization. Results demonstrate that the contact stress values on the ball key, inner raceway, and outer raceway are concentrative. The ball key is the most dangerous part of the flexible joint, and its safety can be improved by increasing its diameter. When the deflection angle between the flexible joint was increased from 0 ° to 18 °, the contact stress value also increased to 220 MPa. However, the contact position was random on the inside of deflection. The proposed method provides a good prospect to optimize the structure parameters of the flexible joint and ultra-short-radius drilling parameters