This paper presents the results obtained by a generalized cut cells strategy on 3-D blast waves problems. The mesh is cartesian except when it is intersected by the surface of the solids inserted in the computational domain. The improvement, relatively to a classical cut-cells method, is the treatment of the cut which preserves the real geometry of the surface instead of approximating it by a plane. This approach avoids a loss of precision of the numerical scheme at the boundaries and allows future extension to higher order schemes (> 2). Moreover it is useful for any kind of geometry with a high efficiency in computation time. The drawback is the complexity of the geometrical problems which can rise because of the diversity of situations in the treatment of the cuts. The performance of the approach is tested on a few examples allowing comparisons with experiments or other techniques and physical discussions.