This study aims at free vibration of stiffened thin open-curved shells with parabolic curvatures. The shells have a curvature with variable radii in one direction. Different stiffening configurations that are usually applied in local ship structures, including un-stiffened, longitudinally stiffened, transversely stiffened, and orthogonally stiffened shells are studied. The energy relationship is derived by using the first-order shell theory as well as implementing the assumptions of global vibration mode. Natural frequencies and mode shapes related to the first five vibrational modes are extracted using extended Kantorovich–Ritz method (EKRM). The results of the EKRM were validated against those obtained by the Finite Element Method (FEM). The EKRM was found to have appropriate convergence and accuracy from the viewpoints of the natural frequencies and mode shapes.