This paper is devoted to analytical modelling and numerical simulation of the so-called pumping kite wind generator whose operating principle is to mechanically drive a groundbased electric generator using tethered kites. On the basis of the refined crosswind motion law, the mathematical model of steady crosswind motion of the tethered kite is constructed. Necessary conditions for optimality of the mean mechanical power functional are derived. Optimal control of the tether length rate is studied for the cases of open-loop and closed-loop figure-of-eight trajectories. The performance coefficient of the pumping kite wind generator is introduced. Simple formulas for the mechanical power output are obtained. (C) 2009 Elsevier Ltd. All rights reserved.