Parallel architecture computers are, or rather will be, a great asset for structural non-linear analyses. The proposed approach is first and foremost dedicated to the field of Mechanics: it is a ‘parallel’ approach to plasticity and viscoplasticity problems in the case of small displacements. This approach can be put into the family of domain decomposition methods, which is well suited to multiprocessor computers with distributed memory. A partition of the structure is introduced from two entities: substructures and interfaces. Each substructure is considered as a structure on its own; it communicates only with its neighbouring interfaces. Interfaces are bidimensional entities with their own behaviour (unilateral contact, perfect interface, ...). This decomposition is integrated into a large time increment approach in order to solve the mechanical problem. This last step is a general method that deals with time-dependent, non-linear problems, and has recently been proposed. The first applications (without concern for decomposition into substructures), in the cases of plastic and viscoplastic behaviours, have shown the efficiency of the strategy. Its original feature is to treat the history of the unknowns in a single large time increment, without any a priori assumption on their time evolution. A second point is that this strategy takes into account the properties of the mechanical equations in order to separate them into two groups: linear, and possibly global, equations on the one hand; and local, and possibly non-linear, equations on the other. In association with the structural decomposition, the large time increment method can take advantage of the intrinsic parallelism of the problem; the global and linear problems to be solved are independent of each substructure. The convergence of the proposed strategy has been demonstrated under relatively weak assumptions: theoretical results have been established for ‘stable’ materials. The numerical behaviour of the proposed strategy will be shown in the case of linear elasticity on the following supercomputers: nCUBE (with 64 nodes) and iPSC 860 (with 128 nodes), both having distributed memory.