A general method for the design of the magnitude response of 2-D IIR digital filters by using linear programming is presented. The formulation of the linear problem is achieved by developing appropriate linear constraints which ensure the minimization of a realistic approximation error of the magnitude response. Moreover, the stability of the resultant filter is guaranteed and the computational cost is decreased by exploiting the symmetries appearing in the linear programming problem. The method leads to satisfactory designs as shown with two examples.