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Multi-mobile robot systems (MMRSs) show great advantages over one single robot in many applications. However, the robots are required to form desired task-specified formations, making feasible motions decrease significantly. Thus, it is challenging to determine whether the robots can pass through an obstructed environment under formation constraints, especially in an obstacle-rich environment. Furthermore, is there an optimal path for the robots? To deal with the two problems, a novel graph-based motion planner is proposed in this article. Valid configurations of the system are defined to satisfy both formation and obstacle constraints. Then, the whole valid configuration space is identified and mapped to an undirected graph. The breadth-first search (BFS) method is employed on the graph to answer the question of whether there is a feasible path on the graph. Finally, an optimal path will be planned on the updated graph, considering the cost of path length and formation preference. Simulation results show that the planner can be applied to get optimal motions of robots under formation constraints in obstacle-rich environments. In addition, different types of constraints are considered to verify the generality.