ABSTRACT: Fin whales Balaenoptera physalus exhibit one of the most extreme feeding methods among aquatic vertebrates. Fin whales, and other rorquals (Balaenopteridae), lunge with their mouth fully agape, thereby generating dynamic pressure to stretch their mouth around a large volume of prey-laden water, which is then filtered by racks of baleen. Despite their large body size, fin whales appear to be limited to short dive durations, likely because of the energetic cost associated with large accelerations of the body during several lunges at depth. Here, we incorporate kinematic data from high-resolution digital tags and morphological data of the engulfment apparatus in a simple mechanical model to estimate the drag acting on a lunge-feeding fin whale. This model also allowed us to quantify the amount of water and prey obtained in a single lunge. Our analysis suggests that the reconfiguration and expansion of the buccal cavity enables an adult fin whale to engulf approximately 60 to 82 m³ of water, a volume greater than its entire body. This large engulfment capacity, however, comes at a high cost because the drag, work against drag, and drag coefficient dramatically increase over the course of a lunge. As a result, kinetic energy is rapidly dissipated from the body, and each subsequent lunge requires acceleration from rest. Despite this high cost, living balaenopterids are not only among the largest animals on earth, but are relatively speciose and exhibit diverse prey preferences. Given this ecological diversity, we frame our results in an evolutionary context, and address the implications of our results for the origin of lunge feeding.