New functionals for thin cylindrical shells and space bars with geometric and dynamic boundary conditions are presented using the Gateaux differential. These functionals are also transformable into the classical potential energy equation. To these functionals variational method is applied, which is a very useful tool in the formulation of mixed finite elements. Element matrices of cylindrical shells and space bars are developed including variation in cross-sectional area in the explicit form using isoparametric finite element formulation. The eccentricity of space bars is included in the formulation of the finite element matrices. A rectangular four-noded shell element and a two-noded straight-circular space bar element have 36 and 24 degrees of freedom, respectively.