The path of dual airfoils in a biplane configuration undergoing a combined, non-sinusoidal pitching and plunging motion is optimized for maximum thrust and/or propulsive efficiency. The non-sinusoidal, periodic flapping motion is described using Non-Uniform Rational B-Splines (NURBS). A gradient based algorithm is then employed for the optimization of the NURBS parameters. Unsteady, low speed laminar flows are computed using a Navier-Stokes solver in a parallel computing environment based on domain decomposition. The numerical evaluation of the gradient vector components, which requires unsteady flow solutions, is also performed in parallel. It is shown that the thrust generation may significantly be increased in comparison to the sinusoidal flapping motion. © 2009 Springer-Verlag Berlin Heidelberg.