This chapter focuses on shock waves and their occurrences and applications in compressible flow. Numerous shock wave relationships that enable the analysis of shock waves are derived and presented in this chapter. Section 5.1 introduces the concepts of shock waves and their applications in aviation, space sciences, pipeline flow, and civil structures. Analysis of normal shock waves using continuity, momentum, energy equations, and equation of state is accomplished in Sect. 5.2, which also presents the relevant shock wave relationships between pressures, temperatures, density, and Mach numbers before and after the shock. This section also looks at star Mach number and Prandtl relationship. Section 5.2 is an extensive section since it also looks at normal shock tables for air, normal shocks occurring in divergent section of Laval nozzles with detailed explanations, and illustrative examples on the location of normal shock along with calculation of exit pressure. This section also explains creation of innovative spreadsheets in locating normal shocks in nozzles. Oblique shocks along with relationships between wave angle, deflection angle, and Mach number are considered in Sect. 5.3. Section 5.3 also looks at oblique shocks occurring at the exit of Laval nozzles. Section 5.4 looks at isentropic compression and expansion that can occur in supersonic flow including Prandtl–Meyer flow, Mach Wave, Mach Angle, Prandtl–Meyer expansion fan, Prandtl–Meyer function and their applications to flow over convex and concave corners. Section 5.4 also examines the formation of expansion fans at the exit of Laval nozzles. Section 5.5 considers moving shock waves with applications to sudden opening and closing of valves. The Rayleigh–Pitot equation for flow rate calculations in supersonic flow is considered in Sect. 5.6.