Stochastic and random integral equations are of great importance that may be used in modeling certain type of problems that contains random process and noise. Therefore, the main objectives of this thesis may be oriented as follows: The first objective is to study the theoretical side of stochastic calculus and stochastic processes, which include the basic definitions and fundamental concepts related to this topic, such as stochastic processes, stochastic differentiation and stochastic integration the existence and uniqueness theorem. The second objective is to compare between stochastic differential and integral equations and then provides analytical methods to evaluate the stochastic integrals. The third objective, which is the main goal, that includes numerical and approximate methods for solving stochastic integral equations in both cases, linear and nonlinear, with some illustrative examples for each case.