The effects of composite and shape memory alloy stiffeners on stability of composite cylindrical shells and rectangular plates subjected to a compressive load are compared. The governing equations for reinforced cylindrical shells are developed based on the Love first approximation theory and smeared stiffeners technique. It is shown that composite stiffeners are more efficient in cylindrical shells, while shape memory alloy stiffeners may be preferable in flat plates or in long shallow shells. It is also proven that shape memory alloy stiffeners increase the upper and lower buckling loads of cylindrical shells modeled as single-degree-of-freedom systems by the same amount.