Many fishes use undulatory fin to propel themselves in the underwater environment. These locomotor mechanisms have a popular interest to many researchers. In the present study, we perform a three-dimensional unsteady computation of an undulatory mechanical fin that is driven by Shape Memory Alloy (SMA). The objective of the computation is to investigate the fluid dynamics of force production associated with the undulatory mechanical fin. An unstructured,grid-based, unsteady Navier-Stokes solver with automatic adaptive remeshing is used to compute the unsteady flow around the fin through five complete cycles. The pressure distribution on fin surface is computed and integrated to provide fin forces which are decomposed into lift and thrust. The velocity field is also computed throughout the swimming cycle. Finally, a comparison is conducted to reveal the dynamics of force generation according to the kinematic parameters of the undulatory fin (amplitude, frequency and wavelength).