Flapping airfoils in a biplane configuration are optimized for a maximum thrust production. A parallel Navier-Stokes solver on overset grids and a gradient based parallel optimization method are employed. The periodic flapping motion of airfoils in a plane configuration is described in a combined pitch and plunge. The pitch and plunge amplitudes and the phase shift between them are optimized for a range of flapping frequencies. It is shown that at low flapping frequencies, flapping airfoils in a biplane configuration produce more thrust than a single flapping airfoil. However, at high flapping frequencies the pitch amplitude tends to go to zero, which promotes an early leading edge vortex formation and limits the thrust production.