Finite element methods (FEM), and its associated computer software have been widely accepted as one of the most effective general tools for solving large-scale, practical engineering and science applications.ย For implicit finite element codes, it is a well-known fact that efficient equation and eigen-solvers play critical roles in solving large-scale, practical engineering/science problems.ย Sparse matrix technologies have been evolved and become mature enough that all popular, commercialized FEM codes have already inserted sparse solvers into their software.ย However, a few FEM books have detailed discussions about Lanczos eigen-solvers, or explain domain decomposition (DD) finite element formulation (including detailed hand-calculator numerical examples) for parallel computing purposes.ย The materials from this book have been evolved over the past several years through the author's research work, and graduate courses Formation of the equations of motion -- Element energy functions -- Introduction to the finite element displacement method -- In-plane vibration of plates -- Vibration of solids -- Flexural vibration of plates -- Vibration of stiffened plates and folded plate structures -- Analysis of free vibration -- Forced response I -- Forced response II -- Computer analysis techniques