This paper analyzes the diffraction of Lamb waves by a finite crack situated on the plane of symmetry of an elastic layer. The surface of the crack and of the layer are assumed to be stress‐free. The problem is solved by the modified Wiener–Hopf technique. The field of the reflected and transmitted waves, and also the field in the vicinity of the crack, are given as an expansion in natural waves of the elastic layer. The amplitudes of these waves are expressed in terms of certain generalized quantities, which are found from exponentially converging infinite systems of equations. The solution converges at any value of the parameterL/H≳0 (whereLis the length of the crack andHis the thickness of the layer) and is particularly effective as this parameter increases. The strongly resonant phenomena in the region of the layer occupied by the crack are identified and discussed.