As discussed in Sect. 2.4, the definitions of the twist and wrench describe the instantaneous velocity (infinitesimal displacement) of a rigid body and the external load applied at it in the framework of screw theory. Also, an example is given to demonstrate their application in describing the degrees of freedom and constraints of a compliant parallel mechanism in Sect. 2.4.3. Further screw theory is utilized to systematically design compliant mechanisms based on the mechanism-equivalence principle. According to this principle, the design of a compliant mechanism can be categorized into two steps: the design of flexible elements and the integration of them. We begin with flexible elements in this chapter and explore their performance both qualitatively and quantitatively through their internal compliance/stiffness. Particularly, flexible elements are categorized according to their feasible degrees of freedom (DOF). Single DOF flexible elements are examined first in Sect. 3.2, followed by multiple DOF flexible elements in Sect. 3.3.