Recent developments in Micro-Aerial Vehicles have stimulated research into insect aerodynamics. DNS studies of insect flight showed the important role of vortex shedding on the performance characteristics of insects. Most airfoils considered where thick and had an unnatural, blunt (elliptic) trailing and/ or leading edge. Experimental results of fixed airfoils also performing at sub-critical Reynolds numbers suggest a significant performance loss due to thickness and blunt leading and trailing edges, since they promote unfavorable separation of the boundary layer. In this study a flapping insect wing is modeled with a sinusoidal plunging airfoil. The corresponding two-dimensional unsteady, incompressible Navier-Stokes equations are solved with respect to a body-fixed coordinate system. This non-inertial coordinate system introduces a body force. The equations are solved with a validated and verified Navier-Stokes solver for Reynolds number 150, Strouhal number 0.25 and dimensionless amplitude (A/c) 1.5. The aerodynamic performance characteristics of a blunt 10% ellipse and N0010 airfoil are compared, statically and dynamically, with the thinner and sharper 2% ellipse, N0002 and N4702 airfoil.