Structural properties of solid N2 and CO2 under pressure have been studied with a recently reported theory. The model allows for calculation of the structure and dissociation energy of molecular crystals, using no empirical parameters where dispersion energy is included as a sum of the pair interactions. Comparison with available low temperature experimental results shows good agreement with average errors in lattice constants of about 1% and in lattice energies of about 6%. Calculations were performed on nitrogen in a number of structures, including the experimentally observed P a3 (α), P42/m n m (γ), P63/m m c (β), and P m3nstructures, as well as a recently proposed structure with space group R3̄m. The R3̄mstructure was found to be more stable than the P a3 structure at about 10 kbar. Calculations were carried out on carbon dioxide in the P a3 structure. Comparison of the calculated pressure‐volume curves with room temperature experimental curves to 100 kbar shows very close agreement for both N2 and CO2.