Biological structures are defined by rigid elements, such as bones, and elastic elements, like muscles and membranes. Computer vision advances have enabled automatic tracking of moving animal skeletal poses. Such developments provide insights into complex time-varying dynamics of biological motion. Conversely, the elastic soft-tissues of organisms, like the nose of elephant seals, or the buccal sac of frogs, are poorly studied and no computer vision methods have been proposed. This leaves major gaps in different areas of biology. In primatology, most critically, the function of air sacs is widely debated; many open questions on the role of air sacs in the evolution of animal communication, including human speech, remain unanswered. To support the dynamic study of soft-tissue structures, we present a toolkit for the automated tracking of semi-circular elastic structures in biological video data. The toolkit contains unsupervised computer vision tools (using Hough transform) and supervised deep learning (by adapting DeepLabCut) methodology to track inflation of laryngeal air sacs or other biological spherical objects (e.g., gular cavities). Confirming the value of elastic kinematic analysis, we show that air sac inflation correlates with acoustic markers that likely inform about body size. Finally, we present a pre-processed audiovisual-kinematic dataset of 7+ hours of closeup audiovisual recordings of siamang (Symphalangus syndactylus) singing. This toolkit (https://github.com/WimPouw/AirSacTracker) aims to revitalize the study of non-skeletal morphological structures across multiple species.