Abstract Given a triangle in the plane, there is a "natural" way to deform it into an equilateral triangle using inner angles. The differential equation of the deformation is a combinatorial analogous to the Ricci flow for Riemannian metrics. We call the equation the combinatorial Ricci flow. The combinatorial Ricci flow can be defined on any surface with a triangulation. We prove that the 2-dimensional combinatorial Ricci flow always converges to the unique metric of constant combinatorial curvature. The later object is closely related to the work of Koebe, Andreev and Thurston on circle packings on surfaces. This is a joint work with B. Chow.