Objective To investigates the stress-strain relationship of ligaments under compression at different strain rates and construct a constitutive model, so as to provide references for prediction of ligament injury and development of replacement materials. Methods The compressive mechanical properties and compressive relaxation responses of rabbit patellar ligaments at different strain rates (0. 001, 0. 01, 0. 1, 1 s-1 ) were tested by universal tensile testing machine, and the corresponding constitutive equations were constructed. Results The uniaxial unconfined compression experiment showed that the stress and tangent modulus under 30% strain and 40% strain increased obviously with the increase of strain rate. Compared with the Gent model, the Fung model and Ogden model were more suitable for fitting the ligament compression curves ( R2 > 0. 99). The four-term Prony series were more suitable for fitting relaxation curves of the ligaments ( R2 > 0. 99). Conclusions The compressive mechanical properties of rabbit patellar ligaments demonstrate the significant viscoelastic response. The Fung model and Ogden model can be used to fit compressive response of the ligaments, and the four-term Prony series can be used to fit the compressive relaxation response of rabbit patellar ligaments.