A modified Gram-Schmidt method was used to obtain the mathematical solution for two boundary value problems of soil water drainage. The flow medium was assumed to be water saturated. Only the steady-state condition was considered. In the first problem the seepage patterns of rainwater flowing through soil were determined. The soil is underlain by an impermeable barrier ata finite depth. A tile drain is half embedded in the impermeable barrier and located directly below furrows in the surface. In the second problem the seepage patterns of rainwater flowing through soil of infinite depth are determined. Water is allowed to stand in the drainage furrows. The solutions were obtained from potential theory by solving Laplace's equation to satisfy an appropriate set of boundary conditons. (Modified author abstract)