For steel flexures, complex geometries are required to reach high support stiffness and limit axis drift over large ranges of motion. These complex flexures are expensive and difficult to manufacture. This paper presents a method of designing short, polymer wire flexures with high support stiffness and modelling their axis drift using a novel method, the arc method. The arc method is validated against finite element methods (FEM) and physical tests, showing at least a factor 10 lower error than existing pseudo-rigid-body models (PRBM) at 70° deflection, while maintaining a simple modelling approach. The use of polymers increases support stiffness of wire flexures by a factor 7800 with respect to steel at 70° deflection, even though the material stiffness is substantially lower. This is due to the large allowed strain of polymers increasing the possible diameter by a factor 110.