Abstract: Polysiloxane rubber is a kind of typical polymer material which is usually colorless and transparent. The molecular structures of Polysiloxane rubber consist of Si——O bonds as the main chain and organic groups directly connected to the silicon atoms, respectively. Owning to the outstanding hyperelastic property derived from the intertwined molecule chains, the polysiloxane rubber is widely used for fabrication of damping structures and stretchable electronics. In engineering application it is crucial to precisely describe the visco-hyperelastic behavior of materials under dynamic and large deformation for the design of polysiloxane rubber based damping structures and flexible electronic devices. Therefore, the visco-hyperelastic property of polysiloxane rubber is systematically investigated in this work. For the first step, the hyperelastic behavior and viscoelastic effect are decoupled to propose the basic forms of the visco-hyperelastic constitutive model. Secondly, the hyperelastic model of the material is established based on quasi-static uniaxial tension, uniaxial compression and planar tension tests, respectively. Then, the strain rate effect is quantified by Hopkinson pressure bar tests, based which the viscoelastic model is established. Accordingly, the visco-hyperelastic constitutive model is finally proposed by combing the two decoupled models. Besides, the proposed visco-hyperelastic constitutive model is used to simulate the drop-weight impact behavior of polysiloxane rubber specimens by finite element method. The well agreement between the simulations and tests show that the viscoelastic constitutive model established in this paper can effectively predict the mechanical behavior of the polysiloxane rubber under impact load, which provides a theoretical and applied basis for the optimal design of polysiloxane rubber based shock absorption structure and flexible electronic devices.