In this paper we propose Gauss-Jordan algorithm using column interchanges for computing a high-order dense matrix inverse produced by the high-order panel method in aerodynamics. The algorithm implements the block cyclic data distribution, which especially has communication advantages for the hypercube network. Results are achieved when running this program on the 4 SGI workstations configured as a 2×2 processor grid. It shows that 57%～64% efficiency can be gained when solving a matrix is about 1000 order.