Rubber mount as an important element can reduce the vibration transmitted by the engine to the frame. And under small and medium deformation conditions, Mooney-Rivlin model can well describe the mechanical properties of the rubber mount. The accurate parameters of Mooney-Rivlin model are the basis of describing the mechanical properties of the mount. First, taking powertrain rubber mount as the research object, the influence of preload on the static characteristics of the mount is studied by the preload test rig. Second, Particle swarm optimization-Back propagation neural network (PSO-BPNN) model and Back propagation neural network (BPNN) model was established. After the number and step length of hidden layer neurons were determined, the prediction accuracy of the two models is compared. Then, combined with finite element analysis and crow search algorithm, a parameter identification model considering preload is established, the constitutive parameters corresponding to preload and non-preload conditions are identified, and the influence of multi-axial load on the identification of constitutive parameters is studied. The results show that: The prediction accuracy and stability of PSO-BPNN model are higher than that of BPNN model. Compared with the constitutive parameters corresponding to the non-preload conditions, the errors of X and Y calculated according to the constitutive parameters identified under the preload conditions are significantly reduced in each working condition, and the errors of each working condition in the three directions are within 15%, which can more accurately describe the mechanical properties of the rubber mount under each working condition.