The distribution of electrical current and the resultant Joule heating in tissues of the human upper extremity for a worst-case hand-to-hand high-voltage electrical shock was modelled by solving the Bioheat equation using the finite element method. The model of the upper extremity included skin, fat, skeletal muscle, and bone. The parameter sets for these tissues included specific thermal and electrical properties and their respective tissue blood flow rates. The extent of heat mediated cellular injury was estimated by using a damage rate equation based on a single energy barrier chemical reaction model. No cellular injury was assumed to occur for temperatures less than 42 degrees C. This model was solved for the duration of Joule heating required to produce membrane damage in cells, termed the lethal time (of contact) for injury. LT's were determined for contact voltages ranging from 5 to 20 kV. For a 10,000 volt electrical shock LT's for skeletal muscle are predicted to be: 0.5 second in the distal forearm, 1.1 second in the mid-forearm, 1.2 second in the proximal elbow, and 2.0 seconds in the mid-arm. This analysis of the electrical shock provides useful insight into the mechanisms of resultant tissue damage and provides important performance guidelines for the development of safety devices.