Numerical methods are indispensable in modern civil engineering, offering powerful solutions to problems that are otherwise unsolvable through traditional analytical techniques. This chapter delves into the core numerical methods used in civil engineering, from linear algebra to differential equations and optimization techniques. The chapter begins by exploring linear algebra methods, including matrix operations and eigenvalue analysis, which are critical for solving systems of equations in structural analysis and fluid dynamics. It progresses into the realm of solving ordinary and partial differential equations, essential for modeling dynamic systems such as soil consolidation, heat transfer, and vibration analysis in structural engineering. Moreover, this chapter introduces optimization techniques, encompassing both unconstrained and constrained methods, that are widely applied in the design and analysis of civil infrastructure. Multi-objective and global optimization methods are also discussed, highlighting their relevance in large-scale engineering projects where conflicting objectives must be balanced. The chapter concludes by demonstrating how MATLAB’s robust numerical computing environment facilitates the efficient implementation of these methods, enabling engineers to tackle complex real-world problems with accuracy and efficiency. By the end of this chapter, readers will have a comprehensive understanding of the essential numerical methods used in civil engineering and the ability to apply them using MATLAB to solve complex engineering challenges.