We present a full three-dimensional electrodynamic model to simulate a photoconductively switched high voltage spark gap. This model describes the electromagnetic field-propagation in a coaxial spark gap set-up, which determines the rise time of the switched pulse and reveals the influence of discontinuities, such as view ports, on the pulse shape and the rise time. Existing inductive lumped element and transmission line models, used to model laser-triggered spark gaps, are compared with our electrodynamic model. The rise time of the switched pulses in the different models does not differ significantly. In the electrodynamic simulation, a curvature of the electric field wave front is visible, resulting from the presence of non-TEM modes near the gap. Furthermore, oscillations on the output signal are revealed. These oscillations are caused by internal reflections on the inner and outer conductors. Our electrodynamic model is able to visualize the rise time evolution by monitoring the electric field-propagation in the gap region. The presence of view ports in the set-up increases the rise time at the output significantly and induces, owing to internal reflections, extra oscillations in the signal.