Mechanical cloaks can hide objects and make them unfeelable by reproducing the surrounding displacement field without the objects and cloaks. In the existing works, mechanical cloaks have been considered for hiding a void, while this work develops a generic method to design cloaks for solids with a given stiffness. As materials with properties beyond natural materials are required to achieve this task, metamaterials with spatially varying microstructures are employed in this work. Similar to the functionally graded material, the present metamaterial has graded stiffness from the cloak to the surrounding region, via graded material volume fractions in the microstructures. Therefore, we present a multiscale topology optimization model that considers the cloak macrostructure and material microstructures, by which concurrent optimization of the structural topology and material properties of mechanical cloaking devices is investigated. The optimization model is implemented via (1) novel mathematical formulations for material microstructures based on the finite element method (FEM) and (2) an extended moving iso-surface threshold (MIST) method with a multi-volume fraction topology update scheme. Numerical examples are provided for multiscale design cases for cloaking a void or stiffer solid (e.g., wood, copper, and diamond), and also include finite element analysis (FEA) of the resulting multiscale metamaterials. •New formulations for designing material microstructure in mechanical cloaking.•Method for concurrent multiscale optimization of cloaking materials and structure.•Generic cloaking design method for hiding voids or solids with given stiffness.