This study aims to develop a precision polishing system with high machining rate efficiency. The system is mainly composed of a loading mechanism, a work piece and a polishing pad with belt-shape. The loading mechanism is to generate a specific pressure distribution between the pad and the work surface.¡@Such a pressure distribution is to render the machining rate distribution, along the contact zone between pad and work surface, capable of compensating the work surface error.¡@With the capability of accurately removing the work surface error left by the previous machining method, this polishing system can improve the form precision of work and become an effective high precision machining tool. In this thesis, the relation between the applied loadings and the pressure distribution were established by the finite element method.¡@A linear model described this relation with the applied loading as the input and the desired pressure distribution as the output. The unknown coefficients of the model were then derived from the simulation data by the finite element method. When a desired pressure distribution was given, the applied loadings could be solved from the model by either the simultaneous equation method or the least squared error method.¡@A main issue to investigate in the study was to examine whether a pressure distribution with an arbitrary wavelength spectrum could be obtained by the proposed scheme. A detailed analysis about the effect of wavelength in pressure distribution on the precision of loading estimation was done. Four conclusions could be made from the study. 1.The proposed polishing system can be applied to a free surface with either concave or convex geometrical features 2.The proposed linear model can suggest proper loadings to generate desired pressure distribution with good precision if the wavelength of pressure distribution is large enough. 3.The Shannon sampling theorem can be used to give a qualitative description of the properness of the model in generating a desired pressure distribution. 4.The proposed polishing method has a high machining repeatability when the operating condition is well controlled.