An analysis is presented for the free vibration of an oblique circular cylindrical shell. For this purpose, the shell is transformed into a circular cylindrical shell of unit axial length by a transformation of variables. The deflection displacements of the transformed shell are expressed in a series of the products of the eigenfunctions of an axial beam and the trigonometric functions of angular coordinate. The dynamical energies of the shell are evaluated, and the frequency equation is derived by the Ritz method. This method is applied to free-clamped oblique shells truncated at the free edge, and the natural frequencies and the mode shapes are calculated numerically up to higher modes.