In order to analyze the complex stress field of LPG tank under fire, the application of Sobolev orthogonal wavelet finite element method on it is studied in depth. First, Sobolev wavelet basis function is established, the B-spline wavelet function with the property of multi-resolution analysis is used as scale function, and the wavelet function and basis function are obtained according to the Sobolev orthogonal wavelet theory. Second, the complex stress wavelet finite element model of LPG tank wall is established by using the Sobolev wavelet basis function as the interpolating. Finally, the simulation analysis based on traditional finite element method and the traditional finite element method are carried out, and the simulation results are verified by the test value, the stress changing rules of LPG tank wall is obtained, numerical results offer good theoretical basis for fire prevention. In addition, the wavelet finite element method can obtained higher computing precision based on the comparison of results obtained from simulation analysis and test.