Finite Difference is an attractive alternative to simulation for the numerical calculation of callable mortgage bond values. Finite Difference is often much faster and more accurate than Monte Carlo simulation, so it would be of great interest to see if the values of callable mortgage bonds, although path dependent, can be found via Finite Difference methods. This is the subject of this chapter, which develops a Finite Difference algorithm for valuing callable mortgage bonds. First, the partial differential equation is developed and discretised. A discussion is then presented on how path dependence is handled via so-called jump conditions. The purpose of this chapter is to demonstrate that Monte Carlo simulation and Finite Difference solutions of the same model yield the same results; therefore, the algorithm is developed with that purpose in mind. The present values and first- and second-order sensitivities confirm that Finite Difference is an attractive alternative to Monte Carlo simulations even though callable mortgage bonds are path-dependent products.