Abstract A study was conducted on three models of the medieval siege engine, the trebuchet. The three models analyzed were the "see-saw", the hinged, and the floating arm trebuchet. Of these models, the mathematical model of each was determined. With his model, the most efficient model was determined to be the floating arm trebuchet, with a range efficiency of 0.8275 and an energy efficiency of 0.8526. The hinged trebuchet achieved efficiencies of 0.8065 for both range and energy efficiency and the "see-saw" with efficiencies of only 0.567 and 0.570, respectively. Then, the floating arm trebuchet's arm length ratio and sling length were then optimized. It was determined that the optimal arm length ratio was approximately 1:2, where the short arm is 1.7 feet and the long arm is 3.3 feet. The optimized sling length was 4.45 feet. Finally, the mathematical models were compared to full scale models. These ranges of the full scale models were surprisingly accurate with what was predicted. The hinged trebuchet model had the largest percentage error at 8.4%.