  The swimming of a deformable planar slab in a viscous incompressible fluid is
studied on the basis of the Navier-Stokes equations. A continuum of plane wave
displacements, symmetric on both sides of the slab and characterized by a
polarization angle, allows optimization of the swimming efficiency with respect
to polarization. The mean swimming velocity and mean rate of dissipation are
calculated to second order in the amplitude of the stroke. The optimum
efficiency depends on the ratio of viscosity and mass density of the fluid. For
high viscosity a stroke is found with significantly higher efficiency than
Taylor's solution for a swimming sheet. For low viscosity the efficiency is
optimal for a nearly irrotational flow pattern.
