This paper presents a method for finding the boundaries of constant gain margin and phase margin of sampled-data control systems. The considered systems are first modified by adding a gain-phase margin tester, then the characteristic equations are formulated and factored into stability equations, and finally the parameter-plane method is used to find the boundaries of constant gain margin and phase margin. The main advantage of the presented method is to obtain complete information about the effects of adjustable and/or variable parameters on gain margins and phase margins.