The design of variable stiffness components is of interest in several applicative contexts. One way to provide large stiffness variation is to use antagonistic stiffness in prestressed elastic systems composed of linear springs. Interestingly, such systems can be designed so that the stiffness in specific directions is only controlled by the prestress within the springs. In the absence of an adequate synthesis method, their exploitation for this purpose however relies today solely on the designer ability to find an arrangement of the springs that meet his requirements in terms of antagonistic stiffness variation. In this paper, a method is introduced for the synthesis of variable stiffness components using prestressed elastic systems. This method takes into account the antagonistic stiffness coming from the prestress and thus provides an efficient way to meet user-defined requirements. Several synthesis problems for usual variable stiffness components are assessed. It shows the effectiveness of the method to provide new arrangements suitable for implementations. The ability of the method to identify alternate arrangements for a given problem is also shown to ease the design, notably by introducing an exploration strategy using a predictor-corrector method.