The liver is the most frequently injured abdominal organ in frontal vehicle collisions. To better predict the liver biomechanical response and injury risk during numerical simulations of traffic accidents, accurate material models of the liver should be incorporated in human finite element (FE) models. This study presents a total of 18 tension tests performed on fresh human samples of liver parenchyma at four loading rates. All these tests were simulated using specimen‐specific FE models. Three different approaches were employed to identify the parameters of a first‐order Ogden material model of liver parenchyma. The FE simulations with model parameters identified using an analytical approach or based on the displacement of optical markers showed a stiffer response and lower failure stress/strain than the FE‐based models. These variations are probably caused by mechanical inhomogeneity of the tissue and possible violations of other assumptions employed in data analysis (e.g. constant cross‐section assumption). The FE‐based optimized models matched the test data well. The material models presented in this study could be easily implemented in human FE models and used to better understand the liver injury mechanism during vehicle collisions.