Effects of hydrodynamic shear on the shape of the endothelial surface are examined based on evaluations of the rate of entropy generation at the cell surface. A linear solution of the flow over a sinusoidally varying endothelial surface is used to evaluate the entropy generation rate on the cell surface for which measured cell dimensions are available. Both the local rate of entropy generation (equivalent to the rate of energy dissipation by viscous shear) at the peak of a cell and the total entropy generation rate over the cell surface are minimized under conditions of a constant cell surface area and a constant cell peak height; which yields horizontal cell dimensions that are close to those obtained experimentally.