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The furrow irrigation system design problem is cast in an optimization setting. A structured problem formulation and a pre-solution analysis procedure is presented. The application of the proposed approach in the detection and removal of constraint redundancy and inconsistency, as well as complications related to scale problems is demonstrated. Key solution features, such as solution existence and (non)uniqueness, constraint activity at the optimum, as well as properties of monotonocity of the functions used in the problem definition are studied. The analysis reduced the problem into a form which is easier to solve. A method-of-multipliers based constrained nonlinear programming (NLP) algorithm is developed for the solution of the minimum cost furrow irrigation design problem. The NLP model includes a subroutine into which the minimum cost design problem is programmed. Solutions of test problems obtained using the NLP model are in good agreement with those obtained using the General INteractive Nonlinear Optimizer (GINO) model. The validity of the numerical solutions of the test problems is further assessed by comparing them with solution features and properties identified in the problem formulation phase.