An accurate model is essential for the numerical simulation of the rock failure occurring under different conditions. However, the expression of the initial compression stage is often overlooked in the widespread constitutive models. In this pursuit, several models considering the initial compression stage were gathered from the previous studies, and a model based on the energy dissipation principle was proposed in the present study. Subsequently, the experimental data of five different types of rock under uniaxial load was collected from the literature to verify the validity of the proposed model, and the performance was compared with the other models. It was found that all the models listed in this study exhibited good performance in expressing the stress-strain curve during the initial compression stage.