This paper describes a computational fluid dynamics (CFD) based investigation of the pectoral fin hydrodynamics of a bluegill sunfish. The pectoral fin of this fish undergoes significant shape-change during its abduction-adduction cycle and the effect of this deformation on the thrust performance remains far from understood. The current study is part of a combined experimental-numerical approach wherein the numerical simulations are being used to examine features and issues that are not easily amenable to the experiments. These numerical simulations are highly challenging and we briefly describe the computational methodology that has been developed to handle such flows. Finally, we describe some of the key computational results including wake vortex topologies and hydrodynamics forces.