After computing the natural frequency of a beam or plate structure with attachment of an elastic support using the finite element method, two numerical methods are utilized to deal with the case of the support occurring in an element. The first approach is to solve eigenvalue problem with the equivalent stiffness matrix, while the other one interpolates the natural frequency with the sensitivities to the support position as well as the related element shape functions. Both methods can gain the frequency without re-meshing the structure. The former is more applicable but less efficient, whereas the latter has a limitation that the structural vibration mode should be unchanged when the support is changed. Illustrative examples show that both the methods have a high accuracy when the stiffness of the elastic support does not change the structural vibration mode in a region.