Based on a matrix partitioning matrix, three parallel algorithms for solving a tridiagonal system on multicomputers are discussed. All are based on the divide-and-conquer principle and designed for the situation in which the number of processors is much smaller than the dimension of the system. These algorithms are the parallel partition LU, the parallel partition hybrid, and the parallel diagonal dominant. These algorithms are derived, discussed, and compared from the point of view of computational and communication complexities. The authors note that the numerical results on a 64-node nCUBE-1 closely match the analytic results presented.