This study investigates the existence and uniqueness of solutions to Volterra integral equations with discontinuous kernels in both linear and nonlinear cases. The problem is two-dimensional, and the collocation method is employed to analyze the equations. The research aims to provide a comprehensive understanding of the solution properties of these integral equations, which are crucial in various mathematical and physical applications. By examining the existence and uniqueness of solutions, this study contributes to the development of numerical methods for solving Volterra integral equations with discontinuous kernels. The findings of this research have the potential to impact various fields, including physics, engineering, and economics, where integral equations play a significant role in modeling complex phenomena.