This paper attempts to indicate how spatial equilibrium models of the Enke-Samuelson variety may be handled as quadratic programming problems. Assuming the existence of linear regional demand and supply relations, models are formulated and algorithms specified which may be used to obtain directly and efficiently the interregional price and flow solutions for the single and multiproduct, n region cases. For each of the specifications the existence, uniqueness and convergence characteristics are investigated and the conditions for obtaining optimum solutions are noted. Illustrative numerical examples are given to reflect the structure of the programming formulation for several alternative spatial models.