Silicon nitride thin films are deposited by plasma-enhanced chemical vapor deposition on (100) and (111) CaF2 crystalline substrates. Delaminated wavy buckles formed during the release of internal compressive stress in the films and the stress releasing processes are observed macroscopically and microscopically. The stress release patterns start from the substrate edges and propagate to the center along defined directions aligned with the crystallographic orientations of the substrate. The stress releasing velocity of SiNx film on (111) CaF2 is larger than that of SiNx film with the same thickness on (100) CaF2. The velocities of SiNx film on both (100) and (111) CaF2 increase with the film thickness. The stress releasing process is initiated when the films are exposed to atmosphere, but it is not a chemical change from x-ray photoelectron spectroscopy.