This paper introduces a method of transmitting actuation forces through soft, curved materials for use in swimming applications. This concept leverages the mechanics of materials to generate highly nonlinear stiffness and buckling behavior that induces an asymmetric paddling gait in the end-effector, a locomotion strategy seen throughout biology. This approach can be used to simplify actuation signals in soft robotic systems. A soft tubular swimming device has thus been developed which utilizes the proposed shape propagation concept; it is actuated by a soft pneumatic actuator which has been adapted to be co-printed within the tubular geometry and change the tube's curvature when inflated. This work is validated experimentally as well as through the use of FEA and dynamic models, which tell us how altering various design geometry and dynamic parameters can play a role in generating non-zero forward thrust and positive work on the environment. The final, 40 mm long prototype reaches 53 mm/s, 1.33 body lengths per second, when swimming underwater.