Measurements of an immature fin whale (Balaenoptera physalus). which died as a result of entrapment in fishing gear near Frenchmans Cove. Newfoundland (47$^\circ$ $9'$ N. 55$^\circ$ $25'$ W), were made to obtain estimates of volume and surface area of the animal. Detailed measurements of the flukes, both planform and sections, were also obtained. A strip theory was developed to calculate the hydrodynamic performance of the whale's flukes as an oscillating propeller. This method is based on linear, two-dimensional, small-amplitude, unsteady hydrofoil theory with correction factors used to acount for the effects of finite span and finite amplitude motion. These correction factors were developed from theoretical results of large-amplitude heaving motion and unsteady lifting-surface theory. A model that makes an estimate of the effects of viscous flow on propeller performance was superimposed on the potential-flow results. This model estimates the drag of the hydrofoil sections by assuming that the drag is similar to that of a hydrofoil section in steady flow. The performance characteristics of the flukes of the fin whale were estimated by using this method. The effects of the different correction factors, and of the frictional drag of the fluke sections, are emphasized. Frictional effects in particular were found to reduce the hydrodynamic efficiency of the flukes significantly. The results are discussed and compared with the known characteristics of fin-whale swimming.