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The Structure and principle of the hydraulic free piston engine (HFPE) is analyzed, and the mathematical model is established according to the feature of the working principle. The transient processes are analyzed through simulation. The result shows that: 1) the working cycle of the HFPE is unsymmetrical, the compression stroke time is 16ms and the expansion stroke time is 10ms. 2) The speed of the power piston is faster than the conventional diesel engine, the maximum speed in the compression stroke is 12m/s and the maximum speed in the expansion stroke is 17m/s. 3) The acceleration is bigger than the conventional engine, the maximum value is 16500m/s2, at the top dead centre and the smallest value is 3500m/s2 at the bottom dead centre.