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Abstract: In a numerical simulation using the finite element method, the mesh has to be fine enough to guarantee the accuracy of the solution. However, a uniformly fine mesh will usually imply a more expensive computation. Mesh adaptation offers an effective compromise, combining a fine mesh with a low computational cost. The h-refinement consists in sub-dividing some meshes, where necessary due to numerical analysis. Some difficulties occur at the interface between two zones with different levels of refinement, if a conformal mesh is required. To maintain the compatibility, the refinement is performed by specific operations. These operations are simple, using triangles or tetrahedra, but are much more complex with a hexahedral mesh. This paper deals with conformal mesh refinement with hexahedra. A new method, which implies the use of tetrahedra and pyramids to connect the zones of different levels of refinement, is proposed. The details of the algorithm used to generate those meshes are presented. This new technique allows h-refinement to be used in numerical simulations based on hexahedra with a conformal finite element method. Finally, some numerical applications show the relevance of this technique in mechanical computation. [Copyright &y& Elsevier]