Structural form-finding methods compute geometries that satisfy static equilibrium under prescribed loads and boundary conditions, and are central to the design of materially efficient form-active structures. The Combinatorial Equilibrium Modeling (CEM) form-finding method enables an intuitive generation of form through direct assignment of member lengths and internal force magnitudes, and is particularly well-suited for structures combining tension and compression elements. Unlike form-finding methods such as the Force Density Method (FDM), however, the CEM does not reduce to a single linear global system of equations. Instead, equilibrium is obtained through a sequential and generally iterative nodal update procedure, which can become computationally expensive for large or highly connected structures. We reformulate the CEM algorithm using message passing, a computational paradigm originating from Graph Neural Networks (GNN) for efficient processing of graph-structured data. By observing that nodal equilibrium calculations correspond directly to neighborhood aggregation operations, message passing enables parallel evaluation of residual force computations within the equilibrium calculation of the CEM algorithm. We introduce three message passing-based variants of CEM (MP-CEM) with increasing levels of parallelism, culminating in a graph-level formulation that extends the original update scheme to allow simultaneous refinement of all nodes with existing coordinate estimates. The proposed approach preserves the intuitive length and force inputs of the CEM, while significantly reducing computational cost. The methods are evaluated on multiple structural case studies with varying topological complexity, demonstrating order of magnitude reductions in iteration count and computation time compared to conventional CEM implementations. By casting the CEM within a message passing framework, this work bridges structural form-finding and graph neural networks, enabling scalable, differentiable, and computationally efficient form-finding suitable for optimization and real-time design applications.