The uncertainty modeling and reliability analysis and the influence on contact static stiffness for ball screw pair with a large number inherently uncertain parameters are very important in engineering. Considering uncertainty of structural parameters and applied loads of ball screw pair,when evaluating the reliability of ball screw pair through traditional methods,structural parameters and applied loads of ball screw pair are supposed to random variables,but the accurate value of distribution parameters can hardly be known in practical engineering. The uncertain parameters and errors of ball screw pair and the load applied and so on are described as interval variables. A contact deformation interval model and an interval method for sensitivity analysis of plate preloaded double-nut ball screw pair are put forward based on Hertz contact theory. According to the contact static stiffness failure criterion of ball screw,a non-probability reliability model of plate preloaded double-nut ball screw pair is established based on interval model. A numerical example has been used to illustrate the proposed method. The result shows that the proposed method is feasible and reasonable and practicable for the contact static stiffness reliability analysis and sensitivity analysis of plate preloaded double-nut ball screw pair.