A code for computing three-dimensional steady Euler equations regions has been developed for supersonic and hypersonic inviscid flows. First-and second-order upwind schemes are used. The algorithm uses cell-centered implicit finite volume method. The flow fields around a secant ogive-cylinder (SOC) and 10° half-angle circular cone are computed and compared against experimental results of other references. Results of the second-order upwind scheme are in good agreement with experimental data except in the flow separation region. In addition, the results indicate that the second-order upwind scheme gives a more accurate pressure distribution on the body than the first-order before sectional separation occurs.