Electrical Surge Arrestors (ESA's) have been used extensively for lightning and EMP protection. These components are characterized by (a) presenting an open circuit (high impedance) below the gap breakdown potential, (b) becoming a virtual short-circuit above the gap breakdown and (c) displaying a significantly higher level of apparent gap breakdown for very fast input voltage rise-times (dv/dt). This paper describes a mathematical model for a spark gap surge arrestor which has been used successfully to characterize ESA response to the following stimulus: 1. Below DC Gap Breakdown 2. At or above Gap Breakdown 3. At high apparent Gap Breakdown voltage as a function of increased rise-time 4. Damped Sinewave Input (below and at Gap Breakdown) 5. Exposed to prompt gamma radiation using a Flash X-Ray source and an electrical input