In this work, we present a high-throughput first-principles study of elastic properties of bulk and monolayer materials mainly using the vdW-DF-optB88 functional. We discuss the trends on the elastic response with respect to changes in dimensionality. We identify a relation between exfoliation energy and elastic constants for layered materials that can help to guide the search for vdW bonding in materials. We also predicted a few novel materials with auxetic behavior. The uncertainty in structural and elastic properties due to the inclusion of vdW interactions is discussed. We investigated 11,067 bulk and 257 monolayer materials. Lastly, we found that the trends in elastic constants for bulk and their monolayer counterparts can be very different. All the computational results are made publicly available at easy-to-use websites: https://www.ctcms.nist.gov/~knc6/JVASP.html
. Our dataset can be used to identify stiff and flexible materials for industrial applications.