Infiltration is a crucial process in various fields such as hydrology, agriculture, urban soils, and particularly for Sustainable Urban Drainage Systems (SUDS) operation. Over the past century, the physics of infiltration has been extensively studied by developing models that estimate the dynamics of infiltration. In this study, three physically-based infiltration models (CH1, CH2, and CH3) have been developed as part of the Canoe Hydrobox (CH) platform, designed to simulate and evaluate the performance of SUDS. The three models rely on similar approaches to the Green-Ampt (GA) model by describing the water flux as the product of the equivalent hydraulic gradient and the equivalent hydraulic conductivity. The models differ in their ways of defining the hydraulic gradient and conductivity from the hydric conditions, soil parameters, and geometric features. The two first models (CH1 and CH2) consider an increase in the hydraulic conductivity with infiltrated water amount, whereas the last model (CH3) considers only the saturated hydraulic conductivity. For the hydraulic gradient, the first model considers the difference between the surface water pressure head and the height of infiltrated water. The other two models consider the difference between the surface water pressure head and the isostatic water pressure head at the surface in equilibrium with the height of infiltrated water. These models were applied to simulate water infiltration processes into dry, wet, and intermediate-wet soils. We compared these results with the numerical solution of the Richards equation using HYDRUS software. The comparison allowed the assessment of the capability of CH models to satisfy the critical principles of soil water infiltration. Subsequently we used the three models to invert six real experimental infiltration data to test their capability to work in inverse mode. The two models (CH1 and CH2) produced specific time-evolution of infiltration rates in disagreement with the physics of water infiltration under regular conditions (e.g., no water repellence). The third model (CH3) performed the best for both direct and indirect modes and is therefore considered as the best candidate. The CH3 model will be implemented in the new version of Canoe Hydrobox (CH) platform. This study provides a basis for further research into hydrological models for SUDS and their hydraulic performance.