Investigation of aquatic animals' locomotion is of great importance due to their high propulsion efficiency. An efficient algorithm considering all effective parameters is needed to understand the hydrodynamic behavior and their propulsive efficiency. In this paper, a robust three-dimensional unsteady panel method in form of a computer software Panel3D® is presented. Since, in the fish propulsion problems, the contribution of pressure forces is mostly dominant rather than viscous effects, using potential methods are often good choice. Implementation of a wake sheet with a time marching algorithm enables us to simulate burst starting problems such as sudden fish swimming or wing movements. Furthermore, to simulate the flexible oscillation of deforming bodies, it is needed to implement three-dimensional flexible panel movements in the solver. The accuracy of the solver was examined with vorticity generation pattern and estimation of propulsion forces of three kinds of fishes. The effect of frequency and phase angle of oscillating motions has been investigated in different cases.