The human tongue is composed of multiple internal muscles that work collaboratively during the production of speech. Assessment of muscle mechanics can help understand the creation of tongue motion, interpret clinical observations, and predict surgical outcomes. Although various methods have been proposed for computing the tongue's motion, associating motion with muscle activity in an interdigitated fiber framework has not been studied. In this work, we aim to develop a method that reveals different tongue muscles' activities in different time phases during speech. We use four-dimensional tagged magnetic resonance (MR) images and static high-resolution MR images to obtain tongue motion and muscle anatomy, respectively. Then we compute strain tensors and local tissue compression along the muscle fiber directions in order to reveal their shortening pattern. This process relies on the support from multiple image analysis methods, including super-resolution volume reconstruction from MR image slices, segmentation of internal muscles, tracking the incompressible motion of tissue points using tagged images, propagation of muscle fiber directions over time, and calculation of strain in the line of action, etc. We evaluated the method on a control subject and two post-glossectomy patients in a controlled speech task. The normal subject's tongue muscle activity shows high correspondence with the production of speech in different time instants, while both patients' muscle activities show different patterns from the control due to their resected tongues. This method shows potential for relating overall tongue motion to particular muscle activity, which may provide novel information for future clinical and scientific studies.