Infiltration models for hydrological applications are developed for rational forms of the soil hydraulic conductivity and moisture retention functions. The models are based on the traveling and kinematic wave solutions of the governing equation that proved to be highly accurate in specific flow conditions. The approximate solutions describe the one-dimensional infiltration into a semi-infinite medium for uniform initial conditions under either a time-dependent flux or a constant head boundary condition. They capture the profile development from early to late time accurately due to the proper derivation of the wetting front speed in terms of the time-varying surface boundary potential and flux rate. Algebraic expressions of theoretical and practical importance are derived in terms of well-defined soil water parameters and include the effect of the antecedent moisture content in a specific fashion. Practical results include simple expressions for the surface moisture variation for variable rainfall patterns, time-to-ponding expressions and infiltration equations that account explicitly for the initial condition, formulas for the depth of the wetting zone, and algebraic equations for parameter estimation of the soil hydraulic parameters by inverse analysis.