- We present a general framework for two-dimensional finite difference modeling of magnetotelluric data in the presence of general anisotropy. Our approach is modular, allowing differential operators for a range of formulations of the governing equations, defined on several possible discrete grids, to be constructed from a basic set of first difference and averaging operators. We specifically consider two formulations of the two-dimensional anisotropic problem, one with Maxwell's equations reduced to a second order system in terms of three coupled electric components, and one in terms of coupled electric and magnetic x-components. Both formulations are discretized on a staggered grid; the second (coupled electric and magnetic) system is also implemented on a grid with fixed nodes (i.e., not staggered). The three implementations are validated and compared using a range of test models, including a half-space with general anisotropy, an infinite fault with axial anisotropy and a simple dyke model. Comparisons to analytic results (for half-space and fault models), and to results from other anisotropic codes, combined with grid-refinement convergence tests, demonstrate that our algorithms are accurate and capable of routine modeling of two-dimensional general anisotropy. These finite difference codes, demonstrating the flexibility of our numerical discretization approach, can be readily applied to other problems.