The problem of crack detection in a two dimensional infinite elastic medium under anti-plane strain is studied. It is assumed that the medium has an internal closed boundary on which the displacements and stresses are known and the crack begins. Using Cauchy's theorem for integration of analytic functions, a simple method capable of determining the parametric equations of each side of the crack, using the corresponding displacements as parameters, is developed. In general, the method is valid for functions which tend to infinity like A + B ln r + O(1/r) as r $\rightarrow \infty $ (A and B are constants) and for finite and infinite cracks. However, the existence of rapidly oscillating integrands makes the method vulnerable to rounding error, particularly in the far field for infinite cracks and near the crack tip for finite cracks. An alternative method for obtaining accurate values of the length and stress intensity factor of a straight finite crack with known inclination is given.