Most soil-water characteristic curve (SWCC) models contain more than three parameters, but these parameters typically do not have a distinct geometric or physical meaning, or the parameters used are inaccurate because of their high reliance on inverse parameter estimation methods. This phenomenon greatly limits the application of SWCC in the study of mechanical and hydraulic properties of unsaturated soils. To explore the nature of SWCC, this paper reexamines the role of the parameters in the two most commonly used SWCC models from the perspective of the relationship between capillary and adsorbed water. A new and flexible SWCC model (named the MVF model) with four parameters is proposed, which can separate the two different regions by physical constraints on the residual saturation Sr and residual suction ψr. Ten published experimental data sets are compiled to evaluate the performance of the MVF model by comparing it with both the existing models and the experimental data. The MVF model shows excellent performance in terms of goodness of fit, and the fitting parameters are provided with a clear geometric meaning, which helps to establish the connection between the basic properties of the soil and the SWCC. This study consolidates the application and reliable determination of SWCC in estimating the mechanical and hydraulic properties of unsaturated soils. •The relationship of capillary and adsorbed water and the role of the fitting parameters for FX and VG models are reviewed.•A flexible modified SWCC model with four fitting parameters based on FX and VG model is proposed.•The physical constraints from residual suction and residual saturation are employed in this study to reduce the uncertainty of the parameters.•The parameters in the proposed model can better capture the features of the SWCC.•A flexible variation on the mathematical form of the model can be applied to bimodal soils.