The transfer matrix method is used to determine the eigenvalues and eigenfunctions needed to obtain the response of nuclear power reactor internals to dynamic excitations. Transfer matrices and delta matrices are developed for a particular closed-cycle pressurized-water-reactor (PWR) configuration. Two cases are studied, 1) where the internals are rigidly supported near the bottom by the vessel walls and 2) where the vessel elastically supports the internals requiring that the combined structure be analyzed. The analysis takes into consideration structures with different cross sections and masses that are connected in series and/or parallel. Results obtained with a digital computer are shown. The method and the results obtained in this paper can be used for a complete reactor dynamical analysis of most PWR internals, since their structures are similar in design.