The stress-deformation behaviors derived from the continuum-lattice thermodynamic approach were applied to estimate the elastic properties of various boron-nitride crystals, such as boron-nitride sheets and nanotubes as well as cubic boron-nitride. The Tersoff and Tersoff-like potentials were used to describe the interatomic bond potential for the boron-nitride crystals. In this study, three sets of the Tersoff potential parameters and two sets of the Tersoff-like potential parameters from the literature were employed. Both the Tersoff potential parameters proposed by Matsunaga et al. and the Tersoff-like potential parameters proposed by Oh were best for estimating the elastic properties of boron-nitride nanotubes, including a sheet. Meanwhile, the elastic constants of c-BN calculated by the Tersoff potential parameters proposed by Sekkal et al. and the Tersofflike potential parameters proposed by Albe and Moller were in good agreement with experimental and other quantumistic calculation results.