Many differential equations defy analytical solution. Still others are such that analytical solutions are onerous. In these cases, a numerical solution is usually the best (and sometimes the only) option. In this chapter, several methods are presented for solving single or multiple ordinary differential equation(s) numerically. Here, only initial value problems (IVPs) are considered, where all necessary information is given at the origin of the independent variable (usually time or distance). The coverage of methods is not complete. Only the more popular methods used in engineering problem solving are considered. These include the Euler, backward Euler, trapezoidal, and Runge-Kutta (RK) methods.