We have developed an alternative to the one-dimensional partial differential equation (PDE) attributed to Richards (1931) that describes unsaturated porous media flow in homogeneous soil layers. Our solution is a set of three ordinary differential equations (ODEs) derived from unsaturated flux and mass conservation principles. We used a hodograph transformation, the Method of Lines, and a finite water-content discretization to produce ODEs that accurately simulate infiltration, falling slugs, and groundwater table dynamic effects on vadose zone fluxes. This formulation, which we refer to as "finite water-content", simulates sharp fronts and is guaranteed to conserve mass using a finite-volume solution. Our ODE solution method is explicitly integrable, does not require iterations and therefore has no convergence limits and is computationally efficient. The method accepts boundary fluxes including arbitrary precipitation, bare soil evaporation, and evapotranspiration. The method can simulate heterogeneous soils using layers. Results are presented in terms of fluxes and water content profiles. Comparing our method against analytical solutions, laboratory data, and the Hydrus-1D solver, we find that predictive performance of our finite water-content ODE method is comparable to or in some cases exceeds that of the solution of Richards' equation, with or without a shallow water table. The presented ODE method is transformative in that it offers accuracy comparable to the Richards (1931) PDE numerical solution, without the numerical complexity, in a form that is robust, continuous, and suitable for use in large watershed and land-atmosphere simulation models, including regional-scale models of coupled climate and hydrology.