Skeletal muscle is widely perceived as nearly incompressible despite the fact that blood and lymphatic vessels within the endomysial and perimysial spaces undergo significant changes in diameter and length during stretch and contraction. These fluid shifts between fascicle and interstitial compartments have proved extremely difficult to measure. In this paper, we propose a theoretical framework based on a space-filling hexagonal fascicle array to provide predictions of the displacement of blood and lymph into and out of the muscle's endomysium and perimysium during stretch and contraction. We also use this model to quantify the distribution of blood and initial lymphatic (IL) vessels within a fascicle and its perimysial space using data for the rat spinotrapezius muscle. On average, there are 11 muscle fibers, 0.4 arteriole/venule pairs, and 0.2 IL vessels per fascicle. The model predicts that the blood volume in the endomysial space increases 24% and decreases 22% for a 20% contraction and stretch, respectively. However, these significant changes in blood volume in the endomysium produce a change of only ∼2% in fascicle cross-sectional area. In contrast, the entire muscle deviates from isovolumetry by 7% and 6% for a 20% contraction and stretch, respectively, largely attributable to the significantly larger blood volume changes that occur in the perimysial space. This suggests that arcade blood vessels in the perimysial space provide the primary pumping action required for the filling and emptying of ILs during muscular contraction and stretch.