In this study, the definition of cracks in the linear theory of elasticity is dealt with. First,
the validity of the assumption made on the continuity of the displacement field outside the
crack is discussed. In the light of this discussion it is argued that the crack problems in elasticity should be defined as traction boundary value problems instead of mixed boundary
value problems. Subsequently, a method is proposed for solving the crack problems as traction boundary value problems. Finally, the contributions of the gradient and nonlocal theories of elasticity to the fracture mechanics are pointed out.