This chapter will present the following: introduction, methodology of composite structure design, basic stress types, laminate theory, rule of mixtures, modeling and finite element analysis, lay-up notation, symmetric and balanced equations, cracking in composites, vibration and damping, smart structures, fatigue, composites versus metals, residual stresses. Composite materials are inherently more complicated in their structures than single phase, one-component materials such as most metals, plastics, and ceramics. The rule of mixtures approach is a useful method in determining the engineering and physical properties of plies in a laminate. Finite element analysis (FEA) allows detailed stress and deformation solutions to complex shapes. The analysis is based on dividing the structure into a large number of small elements and assigning each element the appropriate material properties. The complex nature of composites makes designing composites parts complicated. Therefore, it is important to follow a general plan for design. The plan presented in this chapter has proven to be successful. It first requires, as do most other design systems, the establishment of the functional specifications of the part. Then, various steps in design and analysis are carried out.