A method is presented to determine the vibration response of a solid, elastic, isotropic cylinder with arbitrary length to radius ratio when subject to arbitrary distribution of axisymmetric excitation on its surfaces. In this method, the axial and radial components of displacement are expressed as a sum of two infinite series. Each term in both the series is an exact solution to the governing equations of motion and has a coefficient that is used to satisfy boundary conditions. One series contains Bessel functions that form a complete set in the radial direction and the other contains trigonometric functions that form a complete set in the axial direction. The components of stress are also expressed in terms of complete sets of functions by using the expression for displacement. The coefficients in the series are determined by using the orthogonal properties of the functions to satisfy the boundary conditions in a mean-square-error sense. Numerical results are presented to illustrate the broadband responses of cylinders to uniform and concentrated loads on the flat and curved surfaces. They are in good agreement with results obtained using ATILA-a commercial finite-element software.