We report the first investigation of the structural stabilities and elastic properties of covalent organic frameworks (COFs), a new class of porous crystalline materials. Representative 2D COFs were found to prefer shifted AA stacking, somewhat similar to graphite. The shear moduli of 2D COFs are exceedingly small, suggesting that the layer-layer coupling in 2D COFs is rather weak, and stacking faults may widely exist. Representative 3D COFs were found to exhibit relatively low elastic stiffness overall. In particular, COF-108, the least dense crystal known, exhibits rather low bulk and shear moduli. Our findings provide important structural and physical details to be considered in the further development of COF materials. (c) 2010 Elsevier B. V. All rights reserved.