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In order to solve the matching problem, the mathematic model of starting process of free-piston engine-generator was analyzed. By simplifying the displacement and velocity of the piston, simplified expressions of driving force of linear motor was deduced. The result showed that the larger piston mass could advisably increase inertial force and decrease the minimum starting force, but reduce the maximum speed and slower the starting process. Less frictional coefficient and effective compression ratio could also reduce the starting force. With the simplified formula, the starting process of a prototype free-piston engine-generator was analyzed and the minimum starting force was achieved.