Fin-actuated underwater robots usually control motion by changing the locomotion primitives of the fins, such as frequency, amplitude, phase shift, or in more complicated cases also the angle of attack. Modelling the generated thrust by an oscillating fin results in a highly non-linear model, thus making it difficult to derive a respective inverse model. In this work, we derived a dynamic model relating the generated thrust to the fins oscillating amplitude and frequency, and proposed the associated inverse-model. The proposed model's accuracy is evaluated by comparing both the theoretical and measured generated thrust for various frequencies. Furthermore, using the proposed fin model, we demonstrate hovering experimental results with the robot U-CAT. The results demonstrate the possibility to control fin-actuated vehicles using the proposed model to generate the fins oscillation amplitudes as control input.