Soft robotic actuators are well-suited for interactions with the human body, particularly in rehabilitation applications. The fluidic artificial muscle (FAM), specifically the McKibben FAM, is a type of soft robotic actuator that can be driven either pneumatically or hydraulically, and has potential for use in rehabilitation devices. The force applied by a FAM is well-described by a variety of models, the most common of which is based on the virtual work principle. However, the use of a piston assembly as a hydraulic power source for activation of FAMs has not previously been modeled in detail. This article presents a FAM designed to address the specific needs of a hand rehabilitation device. A syringe pump test bed is used to find and validate a novel volume–strain relationship. The volume–strain relationship remains constant with the coupled piston–FAM system, regardless of load. This confirms a bivariate approach to FAM control which is particularly beneficial in the exoskeleton application as the load varies throughout use. A novel, fixed-end cylindrical model is found to predict the strain of the FAM, given a volume input, regardless of load. For the FAMs tested in this work, the fixed-end cylindrical model improves strain prediction seven-fold when compared with traditional models.