This paper is concerned with accuracy analysis of ultra-precision machine tools. Accuracy analysis is very important in ultra-precision manufacturing in metal cutting as well as machine tools design. A workable method based on variational analysis is presented in this paper. Using this method, we deduce a mathematical model of our ultra-precision aerostatic marble machine tool. Its output accuracy is analyzed here. We also point out the source and explain the physical meaning of machine errors. Finally we discuss its potential application in the design of ultra-precision machine tool.