This work is intended to provide a tool to the design engineer who is dealing with the design of structures subjected to random excitations. In order to increase the usefulness of the tool, other than linearly elastic behavior, no practical limitation is imposed as far as the type, geometry, support conditions, and material are concerned. The dynamic equilibrium equations of the initially stressed structures are obtained in discrete form with the finite element method and the associated Hamiltonian. These equations may be solved in the usual way by finding first the eigenvalues and the eigenvectors of the “free vibrations”, within the frequency range of the expected excitations, and then uncoupling the equations by the normalized eigenvectors. The damping may be represented by the percent of critical damping of the related modeshapes. The uncoupled equations may be handled in the frequency domain by finding the power spectral density functions associated with the random excitations. For this purpose an improved version of the ELAS program is taken to generate stiffness matrices. The program is modified to produce mass and geometric matrices. For the eigenvalue extraction problem, a new algorithm is developed which uses a combination of the inverse iteration with shifts method in conjunction with the Sturm Sequence property. The power spectral density functions of the random, ergodic stationary excitations may be either input or they may be obtained from the histograms of the excitations. The program exploits fully, the symmetry and variable bandwidth property of the assembled matrices, both during the decomposition, and also during the eigenvalue extraction. The input format of the ELAS program is almost left intact. With this software, it is also possible to handle linear buckling and equilibrium problems of the structures. The term structures here means two or three-dimensional trusses, two or three-dimensional frames, gridworks plates, shells (with or without bending), two or three-dimensional elasticity problems, shells of revolution (with or without bending), and solids or revolution.