describe how specific machine components function and how to design or specify them so that they function safely without failing structurally. Although earlier discussion has described structural strength in terms of load or stress versus strength, failure of function for structural reasons may arise from other factors such as excessive deformations or deflections. Here it is assumed that the reader has completed basic courses in statics of rigid bodies and mechanics of materials and is quite familiar with the analysis of loads, and the stresses and deformations associated with the basic load states of simple prismatic elements. we will review and extend these topics briefly. Complete derivations will not be presented here, and the reader is urged to return to basic textbooks and notes on these subjects. This chapter begins with a review of equilibrium and free-body diagrams associated with load-carrying components. One must understand the nature of forces before attempting to perform an extensive stress or deflection analysis of a mechanical com- ponent. An extremely useful tool in handling discontinuous loading of structures employs Macaulay or singularity functions. Singularity as applied to the shear forces and bending moments in beams. the use of singularity functions will be expanded to show their real power in handling deflections of complex geometry and statically indeterminate problems. Machine components transmit forces and motion from one point to another. The transmission of force can be envisioned as a flow or force distribution that can be fur- ther visualized by isolating internal surfaces within the component. Force distributed over a surface leads to the concept of stress, stress components, and stress transforma- tions (Mohr’s circle) for all possible surfaces at a point. The remainder of the chapter is devoted to the stresses associated with the basic loading of prismatic elements, such as uniform loading, bending, and torsion, and topics with major design ramifications such as stress concentrations, thin- and thick-walled pressurized cylinders, rotating rings, press and shrink fits, thermal stresses, curved beams, and contact stresses.