Publisher Summary The purpose of this chapter is to introduce the concept of the finite difference method for finding approximate solutions to plane stress problems with fixed boundaries. The finite difference method is based on the use of the [Φ] matrix. In the finite difference method, the approximate solutions are found by solving a set of algebraic equations that are the discrete representation of the governing differential equations and the boundary conditions. The discrete representation is formed by replacing the derivatives in the governing equations and the boundary conditions with approximations expressed in terms of differences between nodal displacements. The strain gradient notation is used for developing the finite difference method as this notation allows the boundary conditions to be easily validated and irregular meshes to be routinely used.