Boron nitride, like graphene, can be formed as one-atom thick sheets or as nanotubes, then cut into nanoribbons with their atoms arranged in a hexagonal lattice. Two-dimensional hexagonal boron-nitride nanoribbons have been extensively investigated due to their excellent mechanical properties and high thermal conductivity. They also resist chemical change and are unaffected by high temperatures, leading researchers to believe that they could be consummate nanomaterials. The dimensions of boron-nitride nanoribbons as well as the shape of their edges, which may be armchair or zigzag, may affect the overall behavior of the nanoribbons. In the present paper, the mechanical behavior of different sized zigzag and armchair boron nitride nanoribbons is numerically investigated and predicted by using a structural mechanics approach based on the Brenner potential for boron nitride bonds. According to the proposed method, appropriate spring elements are combined in nanoscale in order to simulate the interatomic interactions appearing within boron-nitride nanostructure. The study focuses on the prediction of tensile stress-strain behavior of boron-nitride nanoribbons of different sizes and edge shapes as well as the estimation of significant corresponding material properties such as Young’s modulus, Poisson’s ratio, tensile strength stress and tensile failure strain. The numerical results, which are compared with corresponding data given in the open literature where possible, demonstrate thoroughly the important influence of size and chirality of a narrow boron nitride monolayer on its mechanical behavior.