The aim of this thesis is studying some numerical methods for solving Stochastic Differential Equation. The mathematical preliminary required to understand these numerical methods is proposed. Since many stochastic differential equations do not have explicit solution, Euler-Maruyama and Milstein numerical methods are used. The numerical simulation for different selected examples are implemented. The necessary concluding remarks are provided. The absolute error, the strong convergence error, the weak convergence error and the linear stability for Euler- Maruyama and Milstein's schemes are discussed and supported by numerical test problems. The comparison different type of convergence and error between Euler-Maruyama and Milstein's for some test problems are presented. Some conclusions and comparison in some sense have been presented with discussions. The programs coded in Matlab software are also given with useful discussion.