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This paper proposes a parallel peer-to-peer cooperative algorithm for approximately solving the constrained fixed-orientation two-staged two-dimensional cutting problem. The resolution process is based in three mechanisms: a beam-search search strategy, a strip generation filling procedure, and a upper bound applied for refining the selected paths. The algorithm explores, in parallel, a subset of elite nodes where each processor develops its own path according to its internal lists. the algorithms adapts to the number of processors available on the peer-to-peer platform by backuping the plateform the partial solutions. The computational investigation on the P2Pdc environment shows the good efficiency of the proposed algorithm.