The elastic and failure properties of a typical clay, illite, are investigated using molecular simulation. We employ a reactive (ReaxFF) and a non-reactive (ClayFF) force field to assess the elastic properties of the clay. As far as failure is concerned, ReaxFF was used throughout the study; however, some calculations were also performed with ClayFF. A crack parallel to the clay layers is found to have low fracture resistance when submitted to a tensile loading perpendicular to the crack. The mechanism of both yield and fracture failures is decohesion in the interlayer space. In contrast, under shear loading, the nanoscale failure mechanism is a stick-slip between clay layers. No fracture propagation is observed as the clay layers slide on top of each other. The low fracture resistance in mode I and the stick-slip failure in mode II are both the consequence of the lack of chemical bonds between clay layers where the cohesion is provided by non-covalent interactions. This work, which provides a description of the failure of clays at the microscopic scale, is the first step towards describing the failure of clays at a larger scale where the polycrystalline distribution of clay grains must be taken into account.