The pore-size distributions play a critical role in the determination of the properties of nanoporous cellular materials like aerogels. In this paper, we propose a micromechanical model, and by further designing artificial normal pore-size distributions, we inspect their effect on the macroscopic stress-strain curves. We show that the location of the mean pore size as well as the broadness of the distribution strongly affects the overall macroscopic behavior. Moreover, we also show that by using different damage criteria within the proposed model, the elastic, inelastic, and brittle nature of the macroscopic material can be captured. The damage criteria are based on the different modes of deformation in the pore walls, namely, elastic buckling, irreversible bending and brittle collapse under compression, and combined bending and stretching under tension. The proposed model approach serves as a reverse engineering tool to develop cellular solids with desired mechanical properties.