Lattice spring models (LSMs), being simple to implement, have been employed to simulate the elastic and fracture behaviors of materials. However, previous studies have mainly focused on the infinitesimal deformation range, and the applicability of LSMs for large deformations has not been thoroughly investigated. In this study, we systematically study the nonlinearity and anisotropy of elastic responses at a finite strain range as well as the fracture behaviors of two-dimensional triangular and square LSMs (tLSM and sLSM). We show that the mechanical responses of perfect lattices for both LSMs can be exactly predicted analytically. We also investigate the fracture behaviors of pre-cracked specimens under three-point bending, mode-I fracture, and shear fracture loading modes by varying the orientation of the crack with respect to the lattice. Our results on both perfect and pre-cracked lattices indicate that the mechanical properties of the sLSM is significantly more isotropic than the tLSM.