This chapter describes the application of the finite difference method, orthogonal collocation method, and initial value methods to the flow of fluids. The first problem is the flow of two fluids in pipes and annuli. Then the flow of polymers in pipes is described; these problems are made complicated because the viscosity of a polymer depends on the shear rate, and the shear rate varies with the radial position in the pipe. Boundary layer flow involves a semi-infinite domain, and a tank drainage problem involves integrating an initial value problems. All these problems except the tank drainage problem are boundary value problems. Two and three dimensional flow problems are usually done with a commercial simulator, and they are not treated in this chapter.