A compliant mechanism transmits motion and force by deformation of its flexible members. It has no relative moving parts and thus involves no wear, lubrication, noise, and backlash. Compliant mechanisms aims to maximize flexibility while maintaining sufficient stiffness so that satisfactory output motion can be achieved. When designing compliant mechanisms, the resulting shapes sometimes lead to rigid-body type linkages where compliance and rotation is lumped at a few flexural pivots. These flexural pivots are prone to stress concentration and thus limit compliant mechanisms to applications that only require small-deflected motion. To overcome this problem, a systematic design method is presented to synthesize the shape of a compliant mechanism so that compliance is distributed more uniformly over the mechanism. With a selected topology and load conditions, this method characterizes the free geometric shape of a compliant segment by its rotation and thickness functions. These two are referred as intrinsic functions and they describe the shape continuously within the segment so there is no abrupt change in geometry. Optimization problems can be conveniently formulated with cusps and intersecting loops naturally circumvented. To facilitate the optimization process, a numerical algorithm based on the generalized shooting method will be presented to solve for the deflected shape. Illustrative examples will demonstrate that through the proposed design method, compliant mechanisms with distributed compliance will lessen stress concentration so they can be more robust and have larger deflected range. It is expected that the method can be applied to design compliant mechanisms that have a wide variety of applications from precision instruments to biomedical devices.