Classical fracture theory is formulated within classical continuum mechanics and possess singularities at the dislocation cores as well as crack tips. A number of generalized continuum theories successfully regularize the field quantities such as stress and/or strain. Nevertheless, these generalized theories should be selected carefully, in fact to improve our fracture theory towards realistic situations. Validation with experimental observations as well as numerical experiments can guide us through this selection. Atomistic simulation is capable of providing us details of the field quantities at the vicinity of crack tips. In this presentation, we compare quantities such as the stress field of a crack within nonlocal and gradient elasticity theories with results from atomistic simulations. Besides qualitative agreement, such comparisons can also provide tools to evaluate the internal length scale parameters of the generalized continua.