The paper describes two devices with inventor’s certificates enabling to increase the determination accuracy of the composite materials strength characteristics according to tubular specimens test results. The test results are provided. To prevent the loss of tubular specimen stability unilateral connections are used in devices. These connections are constrained either outside or inside of the shell. To account for the unilateral links effect a calculation diagram, which allows us to describe the shell stability loss by relatively simple analytical ratios that allow visually to present the features of tube sample being compressed, is used. The paper presents in theoretical terms how much the critical load of a compressed cylindrical shell with unilateral constraints increases. According to the authors the difference between cylindrical shells with unilateral constraints and the shells with bilateral constraint is described for the first time.