In this paper, we develop a mathematical model of dynamic flows in steam supply networks that include multiple plants producing, consuming, and interchanging steam. This type of steam supply networks have been recently addressed in practice and become significant in the context of energy systems integration. The model contains dynamic characteristics of the steam boilers and the steam transporting pipes as well as a graph-theoretic property of the steam supply networks. We then perform a theoretical analysis of the derived model based on the graph-based formulation. A set of non-isolated equilibrium points is located and proved to form a normally hyperbolic invariant manifold under certain conditions. Its physical meaning and implications are illustrated by a numerical example with a three-plants loop model.