The equation governing isothermal flow of water in deformable media is one of mass conservation. For an appropriately small volume element satisfying certain averaging criteria, the conservation equation helps convert the rate of accumulation of mass to an equivalent, average time-derivative of the potential function. The goal of numerical modeling is to evaluate the rate of mass accumulation in the volume element by integration in space and time. In order to carry out the integration, the flow region has to be partitioned and spatial gradients of potential evaluated. Depending on the procedure by which spatial partitioning is achieved and on the manner in which potential gradients are evaluated, different numerical schemes such as the integral finite difference method and the finite element method arise. These methods can lead to a set of either explicit or implicit discretized equations. In setting up the equations, time-dependent coefficients may be handled in either a quasi-linear or an iterative fashion. The final set of implicit equations, giving rise to a sparse coefficient matrix, may be handled through direct solvers or through iterative solvers. Numerical models may be validated with the help of analytic solutions to partial differential equations or with experimental data. Based on set-theoretic concepts, it is reasoned that numerical models possess far greater generality than merely providing analytic solutions to the partial differential equation. To derive the real benefit of numerical models, therefore, techniques should be developed to validate numerical solutions based on their own axiomatic foundations, rather than relying upon analytic solutions. Although our current computing abilities transcend our ability to generate sophisticated field data, there is considerable scope for further research on numerical methods. Among new areas of research one could include: (a) incorporating the algebra of probabilistic distributions into existing deterministic models, and (b) developing new techniques to validate numerical models in their own right.