The problem of diffraction of normally incident longitudinal and antiplane shear waves by two parallel and coplanar Griffith cracks embedded in an infinite, isotropic and homogeneous elastic medium is solved. Approximate formulas are derived for the displacement field, stress tensor, stress intensity factors, farfield amplitudes and scattering cross section when the wave lengths are large compared to the distance between the outer edges of the two cracks. By taking appropriate limits we derive various interesting and new results. Furthermore, we derive the solution of the corresponding problem of diffraction of a plane acoustic wave by two rigid coplanar and parallel strips.