This chapter presents a thorough examination of the Finite Difference Method (FDM), including its various types along with significant applications in finance. The Finite Difference Method (FDM) is a robust numerical technique employed to solve differential equations by approximating derivatives using finite differences. The exploration starts with the fundamental principles of FDM and its relevance in mathematical modeling, supported by relevant literature. The chapter then delves into different types of FDM, including explicit, implicit, and Crank-Nicolson methods, highlighting their unique characteristics and computational properties. Finally, this paper examines the application of the Finite Difference Method (FDM) in the domain of finance, with a particular focus on the pricing of derivative securities such as options. The analysis evaluates the effectiveness and efficiency of FDM in modeling and capturing complex financial phenomena. This evaluation is substantiated through relevant examples and case studies, providing a comprehensive understanding of FDM's practical applications in financial modeling. This thorough examination highlights the significance of FDM (Finite Difference Method) in financial modelling and its potential for future advancement in computational finance.