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. The overall computational approach is applied to the structural analysis of the cabin of a launch vehicle on the iPSC/860. Numerical and performance results are reported and discussed in details. They demonstrate the potential of the methodology for the parallel solution of realistic structural mechanics problems.