A general first-order elastic theory is presented which enables the eigenfunctions and eigenfrequencies of a perturbed sys- tem to be computed easily and accurately from the solutions of the unperturbed problem. As an example of the application of the theory, the eigenfrequencies of an N-electrode monolithic quartz crystal filter are found, starting from the known solutions of the single- electrode resonator. For this problem the eigenfrequency separation is given explicitly in terms of the configuration of the filter and the one-electrode eigenfunctions. The results obtained are compared with those obtained by standard wave-theory, and very close agree- ment is found. UK,VK,WK NOhIENCLATURE normalization coefficient of the elastic eigenfunctions. normalized electrode length (electrode lengthlplate thickness). geometric mean of the electrode lengths. thickness of the quartz plate. elastic constant. normalized gap (distance between the edges of the electrodes). normalized distance between the centers of the electrodes. wave number of the thickness-twist solu- tion for the single electrode problem. number of electrodes. stress tensor. zero order components of the displace- rnent in the i, 2, and 3 directions for the Kth mode. perturbed components of the displace- ment in the i, 2, and 3 directions for the Kth mode. volume of the elastic body. expansion parameter wave numbers of the thickness-twist' solut.ion for the single electrode problem. Voigt's face-shear modulus strain tensor. Kronecker delta. shifting of the eigenfrequencies.