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We present(1)the dynamical equations of deforming body and(2)an integrated method for deforming body dynamics and unsteady fluid dynamics,to investigate a modelled freely serf-propelled fish.The theoretical model and practical method is applicable for studies on the general mechanics of animal locomotion such as flying in air and swimming in water,particularly of free self-propulsion.The present results behave more credibly than the previous numerical studies and are close to the experimental results,and the aligned vortices patte is discovered in cruising swimming.