The three-dimensional flowfield around blunted bodies traveling at supersonic speed is computed using a time-dependent technique. A similar technique has been used by one of the present authors to compute two-dimensional and axisymmetric flowfields around blunted bodies and has proved to be highly successful when compared with experimental results. The problem is mathematically well posed, the technique is stable, and its accuracy increases with the fineness of the mesh. Values at points within the shock layer are computed with a method closely related to the Lax-Wendroff technique. The shock wave, however, is considered as a moving discontinuity. Values at shock points and at body points are computed by a four-dimensional method of characteristics. In this way, the shock points are defined precisely, and the application of boundary conditions on bodies of any shape becomes easy. In addition, a drastic reduction in computational time is achieved. A three-dimensional flow around a blunt body can be evaluated in 40 min on an IBM 7094 computer. Full detailed examples of computed flowfields are shown.