Abstract: In this study, we evaluate the buckling load with energy approach with finite element models for mechanical buckling analysis of Functionally Graded Materials (FGMs) variable thickness cylindrical shell with initial imperfection. By defining the shell, mathematical equations are obtained which are dominating on the displacement of the shell, using third order shear deformation theory and Von Karman-type kinematic nonlinearity relationships. Considering cylindrical shell properties, so that, the function of properties change is considered as exponential function and variable properties are in the line with the thickness and variable length, the research continues and by applying a mechanical force in the longitudinal direction of the shell, strain-displacement relations and external load research in to the shell and bearing in mind the lasting relationship, the nonlinear finite element model of the relationship of the cylindrical shell of FGM variable thickness with initial imperfection will be defined. Using picard numerical iterative method, nonlinear finite element model of the problem will be solved and then using the Budiansky’s criterion, critical buckling load is achieved. Simultaneous with the critical buckling load, another objective should be minimized like weight and cost of manufacturing cylindrical shell. Therefore, multi-objective optimization problem is defined in which using the genetic algorithm method such goals can be achieved, namely, maximum critical buckling load and minimum weight of the shell and are shown in Pareto Front diagram.