This paper presents the three-dimensional free vibration analysis of solid circular cylinders with any lengths and arbitrary boundary conditions using the B-spline Ritz method based on the theory of elasticity. The proposed method is formulated by the Ritz procedure with the double series of B-spline functions as amplitude displacements and the Fourier series. To demonstrate the convergence and accuracy of the present method, several examples are solved, and the results are compared with other published solutions by the Ritz method with global functions based on the theory of elasticity. Rapid, stable convergence and excellent upper bound solution are obtained by the present method. Moreover, the effects of length-radius ratio and circumferential wave number on frequency parameters of solid circular cylinders having clamped and stress free boundary conditions are also investigated.