In this paper, we propose a numerical method on how to solve a free boundary problem of an anisotropic elliptic partial differential equation in two dimensions. For one-dimensional problems, we can afford to use a direct discretization since the storage is not a main concern. The discretized non-linear system of equations is solved using a Brydon’s updating method. For two-dimensional problems, as a common practice, we transform the free boundary problem to an optimization problem. Numerically, we approximate the free boundary as a line or quadratic curve and utilize a quasi-Newton type iteration. The main cost of the algorithm is to solve an anisotropic elliptic partial differential equation on an irregular domain using the augmented immersed interface method. Numerical examples show the efficiency of the numerical methods.