Over short time scales, muscle fibres maintain a nearly constant volume of intracellular fluid. This fluid is essential to normal biochemical function, but its role in determining the mechanical properties of muscle has been considered in only a few theoretical analyses. Here we investigate the mechanical role of fluid in a fundamental property of muscle, its development of passive tension in response to stretch. We test a model of muscle structure in which incompressible fluid directly influences passive tension by constraining the geometry of intramuscular connective tissues. This interaction is demonstrated using a simple physical model of muscle morphology comprising a fluid-filled bladder wrapped by helical fibres. The behaviour of the model is compared with that of isolated bullfrog muscle subjected to an osmotic perturbation of intracellular fluid volume. Increasing muscle volume by 40% resulted in 69% increased passive tension, occurring in a manner consistent with the behaviour of the model. These observations support the notion that the interaction of connective tissues with the muscle fibres they surround influences the mechanical behaviour of whole muscles, and highlight the role of fluid as a mechanical component of muscle.