Abstract Clay rocks are multiphase porous media having a complex structure and behaviour characterised by heterogeneity, damage and viscosity, existing on a wide range of scales. The mesoscopic scale of mineral inclusions embedded in a clay matrix has an important role in the mechanisms of deformation under mechanical loading by cracking and creeping. This study introduces a micromechanical approach to model the time‐dependent mechanical behaviour of clay rocks. A heterogeneous clay rock is represented at the mesoscopic scale as a composite material consisting of rigid elastic mineral inclusions (quartz, calcite and pyrite) embedded in a clay matrix. To describe the damageable rock behaviour and its failure modes at the small scale, interfaces between different mineral phases and within the clay matrix are considered. Viscous effects are incorporated inside the clay aggregates, with intergranular microfractures propagating in the clay matrix, in order to investigate their contribution to the creep behaviour of clay rock at the macroscale. The mesostructure of the clay rock is represented in digital 2D Representative Elementary Areas (REAs). The overall mesoscale behaviour of the clay rock under mechanical solicitation is numerically obtained from the REA by computational homogenisation within a two‐scale finite element squared framework. Then, the model is validated at mesoscale against experimental data. The variability of the material response and the time evolution of the mineral interfacial damage state are investigated in relation to the small‐scale properties and failure, while considering mesostructure variability. The results can give some valuable insights into creep behaviour of the clay rock from a small‐scale perspective.