We have developed a novel type of submersible named the Synergistically Propelled Ichthyoid (SPI). The SPI is propelled by the synergistic combination of jet action and oscillatory motion of a fluttering fluid-conveying tail. Two dynamic models for an SPI are presented and solved: an analytically tractable model and a more complex model that captures the complete dynamics in two dimensions. The latter model has been solved numerically—these simulations show a benefit of using a fluttering tail relative to a dimensionally identical rigid tail. Construction details of an experimental realization are provided, and preliminary measurements taken using that platform are also provided. These measurements qualitatively confirm the simulation’s conclusion that a fluttering flexible tail is capable of higher speed than a dimensionally identical rigid tail.