The two-dimensional problem of tile drainage on sloping heterogeneous lands was considered. The land surface and the impermeable boundaries of the problem were of a general shape. The flow in both the saturated and unsaturated zones was considered and the system was treated as one composite system. The problem was solved by a finite difference numerical method using the successive over-relaxation iterative (SOR) method for the steady state case with no local recharge, and a combined Newton inner iteration and successive over-relaxation outer iteration for the transient state case with local recharge. Both the rising water table and the falling water table cases were simulated. A computer program was written in Fortrain IV language for this purpose, and a UNIVAC 1108 computer system was used. The results of two runs for a hypothetical problem and one run for a field testing problem are presented. The results were compared with some approximate mathematical solutions for the falling water table.