Finite Element Method (FEM) is a well-established numerical technique for analyzing the structural behavior of mechanical components and systems, as well as for use in solving problems in heat transfer, fluid flow, and electromagnetic potential. The method has become increasingly popular in recent years due to rapidly evolving, sophisticated, affordable software that can be easily run on a desktop computer. This two volume work will cover the basics of solid FEM modeling as well as advanced applications in structural dynamics and probabilistic design analysis. The first volume covers the basic background and mathematical principles involved, including numerical analysis and solving simultaneous algebraic equations. Simple applciations in solid modeing, using the popular program ANSYS are offered as well.