The computation of the multidimensional determinant can be required in different actual tasks. It reduces to the full graph traversal. As the dimension and the order of multidimensional matrix grow, the computation of the determinant becomes more bulkier and time of computation grows rapidly. Nowadays the rise of the performance of the computing devices is being gained by an increase in the number of computational cores. All the factors listed above give sense to the paralleling of computations. It allows us to reduce the time of calculation and to consider the cases when the computation without the paralleling would require a lot of time. In this very work, the algorithm of computation of the multidimensional determinant and its sequential program implementation are considered. Also, several parallel algorithms and their program implementations are described. The efficiency of the proposed algorithms is defined by the time of their work with different combinations of values of the order and the dimension of the multidimensional matrix. Also, the comparisons of the parallel algorithms with the sequential algorithm and with each other is made. As the research showed, the paralleling of computations had given a good result in solving this problem and had allowed to quickening the time of calculation for all the parallel algorithms. Not all the parallel algorithms showed equal results though: it might be connected with the features of the chosen computing platform. It has been experimentally defined that the complication of the algorithms might not lead to the growth of its efficiency. The home notebook is used as a computational platform. All the calculations were made in programs that had been written in C#.