Supersonic flows over an EFP(explosively formed projectile) have been calculated by a high-order conservation law scheme and two-layer $$textsc{k}$-{varepsilon}$</TEX> model on hybrid viscous unstructured mesh. To verify the accuracy and robustness of the developed code, two basic flows about airfoils are computed and results are compared with existing experimental data and computational results. The comparisons confirm the validity of the code and justify our use for such a highly supersonic and viscous flow over a blunt body. Complex flow features of supersonic flows over an EFP are clearly captured and show agreements with the flow visualization. From the interaction of oblique shocks near the surface of flare, flow structures, that were not identified by previous experimental results, are discovered as a result of present computation.