This work will consider the physics of free-surface flow and groundwa- ter flow in a coupled model. Coupled models of such phenomena are not clearly justified, and there is a lack of precision in deriving such a model. The primary aim of this work is to derive a coupled model of Shallow Wa- ter Equations (SWE) and Richards’ Equation (RE) using asymptotic con- siderations. The numerical coupling chosen for the unified model will be explained as a parallel coupling. Additionally, numerical considerations on how to solve this model using Discontinuous Galerkin (DG) methods will be provided. Furthermore, explanations will be given about how informa- tion is exchanged between the two models, which are time-synchronized. The solution of RE coupled with SWE using the mentioned procedure with DG formulation is implemented in RIVAGE (an in-house numerical code based on discontinuous Galerkin method), which is then tested on a numerical problem and validated against an experimental benchmark.