In this paper, four possible CAE analysis methods for calculating critical buckling load and post-buckling permanent deformation after unloading for geometry imperfection sensitive thin shell structures under uniformly distributed loads have been investigated. The typical application is a vehicle roof panel under snow load. The methods include 1) nonlinear static stress analysis, 2) linear Eigen value buckling analysis 3) nonlinear static stress analysis using Riks method with consideration of imperfections, and 4) implicit quasi-static nonlinear stress analysis with consideration of imperfections. Advantage and disadvantage of each method have been discussed. Correlations between each of the method to a physical test are also conducted. Finally, the implicit quasi-static nonlinear stress analysis with consideration of geometry imperfections that are scaled mode shapes from linear Eigen value buckling analysis is preferred.