Many successful models to describe the biomechanical characteristics of planar biological soft tissues are based on strain energy function. However, the parameters in these models are determined by biaxial extension test, which might be difficult to exercise for certain types of soft tissue. This study presents a new constitutive model, the power type strain energy density function model (PTM), and a method to identify its material parameters for rabbit skin using uniaxial extension test of 4-direction strip samples. The abdominal skins from eight rabbits were taken to perform uniaxial tension tests in 7 different directions. The material parameters were identified for each subject based on any 4 out of 7 directions by applying some definite conditions of this issue. For each rabbit, the 35 groups of material parameters were consistent. The 7 material parameters in PTM were identified with root mean square errors <0.061. The results indicate that the material parameters of rabbit skin can be identified from uniaxial extension test data.