I studied the elastic properties of oligoacenes and polycyclic aromatic hydrocarbons crystals within the framework of density functional theory with van der Waals interactions. The full sets of elastic constants were computed. The computed parameters have good agreement with experimental data. The study of four forms (α, β, γ and dimeric) demonstrate that the stacking of molecules leads to different character of interaction between molecules. Crystals with dimeric form have lower anisotropy. If symmetry of crystals is the same, the increase in number of aromatic rings results in anisotropy increase.