The elastic‐wave scattering by a flat crack can be represented by an integral expression involving displacement and strain on the surface of the crack. We have explored the use of a modified static solution as an approximation to the displacement field of a penny‐shape crack in the long‐wavelength regime and then studied numerically how well it connects with the low‐freqency limit of the diffraction regime. Comparisons between this and several other existing approximations are made. We conclude that this quasistatic approximation is useful practically in both the long‐wavelength and beginning diffraction regime.