Kirchhoff’s time‐dependent solution of the wave equation is transformed into a convolution in the time domain, by means of a simple but effective parametrization of a plane‐wave front. It is shown how this representation can be applied to the diffraction of a plane pulse by thin arbitrarily shaped obstacles. The diffracted pulse is shown to depend almost entirely on a single function which can be easily determined from the specified geometry. The general method is then applied to two classical problems: diffraction by a half‐plane and circular screen. The solutions obtained are expressed in terms of elementary functions and are demonstrated to be uniformly valid across shadow boundaries. The method is ideally suited to numerical computation in the case of complicated geometries.