Abstract: The superconducting solenoid magnet is one of the key equipment in the muon ionization cooling experiment (MICE). The coil has an inner diameter of 1 500 mm, length of 285 mm, and is made from copper matrix NbTi conductors with the insulated cross area of 1.65 mm×1.00 mm. The peak magnetic field is up to 7.4 T at a full current of 210 A. In order to reduce mechanical motion of conductors and avoid magnet quench during cooling and charging, the pre-stress is applied to conductor and banding during coil winding process. To solve the confirmation problem of winding pre-stress, the relationship between pre-stress and stress components in cold mass assembly was proposed according to composed cylinder theory. By dynamic simulation of whole processes including winding, cooling and charging by finite element model, the analyses on the stress in cold mass assembly with different pre-stresses on conductor and banding were carried out, and the optimized results of winding pre-stresses for winding the MICE coupling magnet were got.