In this paper, the hygro-elastic behavior of two-dimensional periodic honeycombs composed of multi-layered cell walls is investigated using a computational micromechanics approach. Detailed numerical results for the effective hygro-expansion coefficients and the elastic moduli of honeycombs are obtained. The influence of the arrangement of the cell wall layers and the geometrical parameters of the honeycombs on the effective hygro-elastic properties is examined. Limiting cases are considered, and the validity of the model is established by comparison with the analytical solutions available in the existing literature. The obtained results suggest that the layered architecture of the cell wall enhances the anisotropy in swelling behavior of honeycombs with irregular configuration which is reflected in their transverse hygro-expansion coefficients while regular honeycombs show isotropic behavior. The proposed model explains the complex thermo-hygro-mechanical behavior of natural cellular materials and provides a predictive tool for bio-mimetic material design.