System models consisting of linear partial differential equations which have been put into variational form, can be solved using the finite element method. The construction and use of a special class of one‐ dimensional finite elements, consisting of multiple convolutions of the unit pulse function, is described in this paper. As an example of how to use finite elements, the short circuit and open circuit normal modes of a radially polarized piezoelectric cylindrical shell are obtained. The computional procedures are shown, with special emphasis on how the system matrix equations can beconstructedas well assolvedby the computer. The finite element results are compared to exact values computed by classical methods. Convergence properties with respect to the order of finite elements used and the fineness of the grid structure are examined. Good results are observed for relatively coarse grids with second‐ or third‐order elements.