A variational formulation of thin cylindrically curved panels having transverse displacement and Airy stress function as field variable is presented. Euler-Lagrange equations and boundary conditions are obtained. A finite element based on this variational principle preserving C(1) continuity is formulated. Applications for free vibrations, buckling, and supersonic panel flutter analyses are given. Several numerical calculations are presented. The results obtained are discussed and are compared with previous analytical solutions, numerical calculations, and experimental findings.