Abstarct: In the design of experiments a design called feasible when all of its parameters are estimable, so the distinction feasibility of design is very important in the factor designs. Before now, feasibility criterions of designs have been baxsed on linear models, when designs have a lot of level, criterions of design is very difficult and complicated in linear models baxsed method. The matrix image is a powerful tool to studying this designs without need linear transformation of ANOVA model to judge the feasibility of a designs. The matrix image defines a set that obtained from the columns of a design. In this thesis, feasibility of designs investigating with linear model, orthogonal arrays and matrix image methods, also shown that matrix image baxsed method investigate feasibility of designs easily of other methods.