Vertebrates utilize six extraocular muscles that attach to a tough, protective sclera to rotate the eye. The goal of the study was to describe the maximum tetanic forces, as well as the torques produced by the six extraocular muscles of the piked dogfish Squalus acanthias to understand the forces exerted on the eye. The lateral rectus extraocular muscle of Squalus acanthias was determined to be parallel fibered with the muscle fibers bundled into discrete fascicles. The extraocular muscles attach to the sclera by muscular insertions. The total tensile forces generated by the extraocular muscles ranged from 1.18 N to 2.21 N. The torques of the extraocular muscles ranged from 0.39 N to 2.34 N. The torques were greatest in the principal direction of movement for each specific muscle. The lateral rectus produced the greatest total tensile force, as well as the greatest torque force component, while the medial rectus produced the second greatest. This is likely due to the constant rotational movement of the eye anteriorly and posteriorly to stabilize the visual image, as well as increase the effective visual field during swimming. Rotational forces in dimensions other than the primary direction of movement may contribute to motion in directions other than the principal direction during multi‐muscle contraction that occurs in the vertebrate eye. Anat Rec, 2018. © 2018 Wiley Periodicals, Inc. Anat Rec, 302:837–844, 2019. © 2018 Wiley Periodicals, Inc.