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A saddle-point variational principle is constructed to derive a hybrid substructuring method for the parallel solution of three-dimensional structural mechanics problems. A given mesh is partitioned into disconnected submeshes, and an incomplete solution for the displacement field is first evaluated via a direct method. Next, intersubdomain field continuity is enforced via discrete, polynomial, and/or piece-wise polynomial Lagrange multipliers. The proposed methodology is intrinsically parallel and offers attractive features for distributed memory multiprocessors. A combined r - h adaptive refinement procedure is also developed within the context of this hybrid substructuring method. Its basic features include an element-level error indicator that is based on a parametrized variational principle, a permanent load balancing, and an easily programmable interface gluing.