The purpose of this article is to suggest and demonstrate a procedure for testing economy wide linear programming models.The suggested procedure applies the linear programming model to an historical period. In general, the model's optimal solution will not be identical to the actual historical solution. Differences between the model's optimal and the economy's actual solutions could be explained by alternative sets of hypotheses--on the one hand, market imperfections, and on the other hand, defects in the linear programming model. Ordinary statistical tests could then be applied in testing the alternative hypotheses. In order to demonstrate the procedure, a linear programming model designed for prescribing an optimal economic structure for the Greek economy during the period 1954-61 is presented and tested.