In traffic accidents involving pedestrians or persons riding on bicycles or motorcycles it is frequently very difficult to reconstruct the speeds and motions of the various participants. Simple engineering equations call be written that generally describe the physical aspects of the accident, but often there is not enough information available for the analyst to solve the equations. When this occurs it is possible to conduct a parametric analysis of the accident by defining reasonable upper and lower limits for key variables and then solving the equations. Results from the parametric analysis can be compared with known events related by witnesses and participants and with objective evidence to establish a probable range of conditions that closely define what actually happened in the accident. The technique of parametric analysis will be described and illustrated with actual recent accident reconstructions.