The long-term behavior of dynamical system is usually analyzed by means of basins of attraction (BOA) and most often, in particular, with cell mapping methods that ensure a straightforward technique of approximation. Unfortunately, the construction of BOA requires large resources, especially for higher-dimensional systems, both in terms of computational time and memory space. In this paper, the implementation of cell mapping methods toward a distributed computing is undertaken; a new efficient parallel algorithm for the computation of large-scale BOA is presented herein, also by addressing issues arising from the inner seriality related to the BOA construction. A cell mapping core is thus wrapped in a management shell, and in charge of the core administration, it permits to split over a multicore environment the computing domain, by carrying out an efficient use of the distributed memory. The proposed approach makes use of a double-step algorithm in order to generate, first, the multidimensional BOA of the system and then to evaluate arbitrary 2D Poincar, sections of the hypercube that stores the information. An analysis on a test system is performed by considering different dimensional grids; the effort of a parallel implementation toward medium and large clusters is balanced by a great results in terms of computational speed. The performances are strictly affected not only by the number of cores used to run the code, but in particular in the way they are instructed. To get the best from an implementation on a massive parallel architecture, the processes must be properly balanced between memory operations and numerical integrations. A significant improvement in the elaboration time for a large computing domain is shown, and a comparison with a serial code demonstrates the great potential of the application; the advantages given by the use of parallel reading/writing are also discussed with respect to the BOA grid dimension.