In central receiver systems, the ideal reflective shape of a heliostat is a section of a paraboloid that adapting with the sun's angle and the mirror's location in the field. Deviation from this shape leads to optical astigmatism that increases the spot size on the receiver aperture, which eventually causes higher energy loss and lower conversion efficiency. However, it is challenging to implement the ideal shape by conventional design and manufacturing methods. In this paper, a novel compliant heliostat design methodology is proposed. By tailoring the two dimensional stiffness profile of a square plate, the paraboloid shape can be formed by a simple, low-cost mechanism with concentrated moment loads on the corners of the plate. The static optimized shapes, which can be easily realized by adjusting the loads according to the locations during heliostat assembly on the site, are suggested as approximations of the ideal shapes. Analytical models were developed in detail for the methodology. Numerical analysis consists of finite element analysis, optical ray tracing, and optimization. The numerical results illustrate that the performance of the shape optimized heliostats using tailored stiffness approach is close to the ideal shapes, providing substantial improvement in optical efficiency and reduction in spot size comparing to the flat mirrors. Furthermore, experiments on a prototype heliostat mechanism with a honeycomb-sandwich panel were conducted to validate the effectiveness of this low-cost shaping approach.