Abstract.Let D be an open, bounded, simply-connected region in R 2 with boundary B. Let (x*,y*) be an arbitrary point of D. This paper constructs an algorithm for computing Gauss harmonic formulas for D and the point (x*,y*). Such formulas approximate a harmonic function at (x*,y*)in terms of a linear combination of its boundary values. Such formulas are useful for approximating the solution of the Dirichlet problem, especially when the problem is to be solved many times at the same point with different boundary values.