In this paper we use hypercube computers for solving linear systems. First, the pivoting Guassian elimination is analyzed under two partitioning and two mapping schemes. We then propose solutions for the banded linear system. For the banded system we not only use a hypercube of reduced size but also reduce the execution time. We also present the flow-through method for reducing the size of the local memory of each processor in solving the banded system. Finally, the Jordan-Gauss method, the alternative for solving the linear system, is compared with the Gaussian elimination.