Aim The constitutive model of adipose tissue under medium strain rate and its parameter inversion are studied.Method Based on the published mechanical properties experiments of adipose tissue, the compression experiment of adipose tissue was reconstructed by finite element method, and the parameters of constitutive models of adipose tissue were discussed. Combined with the feasible direction method (MFD) of optimization method, the reverse calculation of parameters of fat tissue constitutive model at medium strain rate was discussed. Results Compared with Ogden constitutive model，the viscoelastic model was more suitable for characterizing the mechanical response at medium strain rate (260s-1). And the parameters of the constitutive model suitable for simulation are obtained using reverse method. Conclusions The viscoelastic model was more suitable for characterizing the mechanical response at medium strain rate. The results can be helpful to study the influence of human adipose tissue on human body injury using finite element simulation in the vehicle collisions.