In this article, semi-analytical 3D elasticity solutions are presented to study the vibration characteristics of two-dimensional functionally graded (2D FGM) metal/ceramic open cylindrical shells under various boundary conditions. In the present formulation, the shell has a smooth variation of volume fractions of metal and ceramic in the radial and axial directions with power law functions. The study is carried out based on the three-dimensional, linear and small strain elasticity theory. The open cylindrical shell is assumed to be simply supported at one pair of opposite edges and arbitrary boundary conditions at the other edges such that trigonometric functions expansion can be used to satisfy the boundary conditions precisely at simply supported edges. The two-dimensional generalized differential quadrature method (GDQM) as an efficient and accurate numerical tool is used to discretize the governing equations and to implement the boundary conditions. The convergence of the method is demonstrated and to validate the results, comparisons are made with the available solutions for FGM cylindrical shells. Results indicate the advantages of using functionally graded open cylindrical shells with graded volume fractions in two directions to a more flexible design than the conventional one-dimensional FGM. The effects of different boundary conditions, various geometrical parameters and volume fraction indices in radial and axial directions on the vibration characteristics of 2D FGM open cylindrical shells are investigated. Finally, frequency parameters of 2D FGM open cylindrical shells are compared with radially and axially conventional FGM.