Porous silica aerogel is an ultra-low-density material with nanostructures that leads to its excellent physio-chemical properties. Considering the characteristics of the material, a micromechanical model to assess the microstructure–property relations is highly demanded. In this study, a cuboctahedron unit cell is proposed as a representative volume element of the silica aerogel to correlate with its density and compressive stress–strain curves. The backbone lattice-structure combined with the dead ends is established to represent the periodic configuration of the aerogel. It is implemented in both the numerical scheme with the finite element method and the analytical model by modifying the Gibson–Ashby model. Furthermore, the crushing behaviors of the material under large deformation are discussed in the numerical study. Due to the features of load-bearing skeletons and non-load-bearing short pillars, the compression process of the silica aerogel exhibits strong nonlinear behaviors. Overall, this computational micromechanics model is capable of accurately simulating the stress–strain curves of silica aerogels with different densities under different loading levels. This work provides a general framework to quantify the microstructure–property relations of porous silica aerogels and also other porous materials.