The Navier–Stokes equations are the most famous and perhaps the most important equations in fluid mechanics. In biofluid mechanics, these equations can be used to compute the flow of air within the airways, the flow of blood in large vessels at sufficiently high shear rates, the flow of urine from the bladder, the flow of crystalloid perfusates in in vitro experiments, and so on. Because few analytical solutions are available, one must often resort to numerical methods to solve these important equations. Two well-known open-source programs for this purpose include SimVascular and CRIMSON. Nevertheless, in this chapter, we will consider five important analytical solutions of the Navier–Stokes equations that describe the flow of Newtonian (viscous) fluids. We will, in addition, consider one illustrative example for a non-Newtonian fluid and one for an inviscid fluid.