Abstract: The fuzzy variational principle (FVP) of solving the critical buckling load of structures is derived by introducing fuzzy parameters into the Rayleigh quotient variation of the critical buckling load. Thereafter, the FVP is used to formulate the fuzzy Ritz method (FRM) and the fuzzy finite element method (FFEM), both of which are able to obtain fuzzy solutions in solving the critical buckling load. Compared with conventional interval methods, the presented two methods circumvent the processes that fuzzy parameters need to be transformed into interval parameters before constructing fuzzy solutions. The present methods significantly reduce computational cost. Numerical examples are employed to illustrate the applicability of the present methods.