Abstract: In order to investigate the fitability in superprecise forming of double curvature panel based on "nails die and vacuum", the approximate generalized Fourier series solution is suggested for the bending problem of the rectangular thin plate supported at arbitrary points with large deflection. The solution is derived by means of the incremental method of load and displacement constraint, which can get the constrained force at the same time for the further iteration of contact state. It is applied to analyze the pattern of the part sinking. The computational results of the plates with several kinds of width and thickness are compared with the experiment. It shows that the accuracy is satisfying well. Finally the proximate range of the critical plate width under varied pressure is suggested and moreover the relevant rules on reduction of errors in fitability are proposed.