Providing realistic interactive simulation requires a powerful animation method with a highly detailed rendering. Based on continuum mechanics, the finite element method needs a volumetric represen- tation of the object to animate. This paper proposes an automatic method for building meshes that are well adapted to interactive simulation starting from miscellaneous input data. Contrary to commonly used methods based on tetrahedral volume meshing, the object is embedded in a regular grid of deformable hexahedra at an arbitrary resolution. This alleviates the complexities and limitations of tetrahedra and results in regular, well-conditioned meshes. Mass and stiffness are set in order to model the physical properties as accurately as possible at any given resolution, in a manner that takes into account the distribution of material within the hexahedra. This allows us to accurately model the mechanical properties of the partially empty boundary hexahedra, and thus enables us to perform fast simulation at a coarse resolution. The accuracy of this approach is compared to theoretical results. In addition, we extend a fast and robust co-rotational approach to the case of hexahedral elements. This permits simulation of arbitrarily complex shapes at interactive rates. We show how to build the hexahedra directly from surfaces and from segmented scanned data, which is very useful to animate complex artistic models or patient specific models for individual medical simulation. Finally, we show how a fast volumetric rendering can make efficient use of the grid structure.