Abstract: The Steiner Problem is motivated by the goal of finding the shortest path network that connects a set of fixed points on a surface. While this problem has been exhaustively investigated in the Euclidean plane, it remains an open problem to solve the Steiner Problem on general non-planar (piecewise smooth) surfaces. We analytically solve the 3-point Steiner Problem on surfaces of revolution by constructing an isometric framework on a plane endowed with a weighted distance metric, thus pioneering new insight into the particularly challenging study of Steiner Problems on surfaces with non-constant curvature.