The cubicorthorhombic shape memory alloy system is studied using a sharp interface model based on the linear theory of compatible laminates. A computational method is developed to generate all possible compatible laminates for a given state of strain, and check whether these laminates satisfy exact compatibility conditions. The type of austenite-martensite interface that can form is dependent upon the detail of the martensite structure; the formation of flat and wedge-like austenitemartensite interfaces is explored. A full search is used to reveal the routes in strain space along which the two-phase structure can continuously evolve. A variety of laminate structures, some well known and some new, are reported. The methods developed are readily applied to other crystal systems, such as the tetragonal crystal system, in shape memory alloys or related materials.