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Objective Vadose zone well (VZW) injection is an effective method of managed aquifer recharge (MAR). To improve VZW injection management, it is of great importance to accurately describe the unsaturated zone properties. Several analytical models have been developed for VZW injection based on the two-parameter constitutive model (Gardner model). As the three-parameter model (MB model) and four-parameter model (MN model) have been proposed, it is of interest to know whether the application of more flexible constitutive models is able to improve the analysis of unsaturated-saturated flow induced by VZW injection. Methods In this study, the MN model (which includes the Gardner model and MB model as subsets) was employed to establish a VZW injection model. The model was solved using COMSOL Multiphysics. The results are utilized to investigate the unsaturated-saturated flow induced by VZW injection for different values of the unsaturated zone properties to analyse the influences of the ground surface flux (GSF), and to compare the hydraulic responses based on different exponential constitutive models. Results The analysis demonstrates that the hydraulic response induced by VZW injection and the influence of ground surface flux are affected by the hydraulic conductivity and the water storage capacity of the unsaturated zone. The relative hydraulic conductivity exponent ωk affects the change in hydraulic conductivity of the unsaturated zone. The moisture retention exponent ωc affects the water storage capacity of the unsaturated zone. The approximation of ωk=ωc=ω will result in some errors in the calculation and prediction of the hydraulic response caused by VZW injection. When the absolute value difference of the pressure head threshold b1=ψa-ψk is small, its effect on the water head increment is small. In this case, it is reasonable to assume that b1=ψa-ψk=0. Conclusion This study can help scholars improve the understanding of the VZW injection process and has important practical significance for the design, implementation and management of injection schemes.