The problem of diffraction of cylindrical and plane SH waves by a finite crack is revisited. We construct an approximate solution by the addition of independent diffracted terms. We start with the derivation of the fundamental case of a semi-infinite crack obtained as a degenerate case of generalized wedge. This building block is then used to compute the diffraction of the main incident waves. The interaction between the opposite edges of the crack is then considered one term at a time until a desired tolerance is reached. We propose a recipe to determine the number of required interactions as a function of frequency. The solution derived with the superposition technique can be applied at low and high frequencies.