In the present paper, the tensile mechanical behavior of different sized, almost squared shaped, boron nitride nanoribbons is numerically investigated and predicted by using a structural mechanics approach based on the use of appropriate nonlinear potential functions concerning both two-body and three-body interatomic interactions appearing within their nanostructure. 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 dimensions of boron-nitride nanoribbons as well as the shape of their edges, which may be armchair or zigzag, have influence on the overall behavior of the nanoribbons. Therefore, the study focuses on the prediction of tensile stress-strain behavior of boron-nitride nanoribbons of different sizes and edge shapes as well as on the estimation of significant corresponding material properties such as Young's modulus, tensile strength, tensile failure strain and tensile toughness. 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.