In this paper we use the time dependent form of the electric field integral equation (EFIE) to solve transient scattering problems for perfectly conducting surfaces. In the computation of scattering from arbitrary surfaces the EFIE has the advantage of being applicable to both open and closed surfaces, whereas the magnetic field integral equation (MFIE) is applicable only to closed surfaces (i.e., solid bodies). On the other hand, for curved surfaces the EFIE is considerably more difficult to apply than the MFIE. This difficulty is primarily due to the occurrence of surface derivatives in the EFIE which are difficult to compute accurately on a curved surface. To overcome this problem in the frequency domain Rao et al. introduced a special set of basis functions defined on a triangular mesh on the surface. With these functions the appropriate derivatives are relatively easy to calculate, and the use of a triangular mesh on the surface means that general open or closed surfaces can be tackled. We use these basis functions together with a time marching method of moments technique to solve the time dependent EFIE. We utilise a particular testing procedure and an averaging technique to overcome the stability problems that time marching methods of solving integral equations are prone to.