A computational study of a periodically pitching and plunging small airfoil in very low Reynolds number flow is presented. The computed vortex structures generated by the airfoil motion are examined, as well as their effects due to pressure distributions around the airfoil. Discussion is presented based upon existing experimental results from open literature, as well as a detailed look at the results of this study. The intended outcome is to produce a computational model that can be utilized in a parametric analysis of flapping modes advantageous to micro-airvehicle development. A large variation in both surface pressure distributions and vortex structures are seen, which correspond to small changes in wing motion. The current methods are capable of capturing these differences, thus allowing the future progression of a parametric analysis to identify lifting and propulsive flapping modes of a small airfoil.