According to the shortcomings of most robot fish,such as not incorporating elastic mechanism to improve energy efficiency and poor pressure resistance capability,squid/cuttlefish,which have excellent swimming capability and pressure-resistant structure,are studied.Swimming mechanism of squid/cuttlefish jetting and fin undulating propulsion is analyzed,and the equations of jet thrust,propulsive efficiency of jetting period and whole hydrodynamic propulsion cycle are given.The advantages of squid/cuttlefish compound swimming are good performance at both high and low speeds,being capable of changing swimming direction immediately,low noise,and that thrust can be generated even if jet velocity is slower than that of the surrounding fluid.In order to explain swimming mechanism in depth,the muscle arrangements and functions of mantle and fin muscular hydrostats,the two locomotory systems,are studied.The muscular hydrostats not only serve to the skeleton support of body,to carry out movement and to generate force,but also have considerable pressure-resistant capability.The hydrostatic pressure in and out of the mantle of most squid/cuttlefish is equal due to no gas filled tissue in their body,which improves their pressure-resistant capability further. During the movement,energetic efficiency is improved because energy is saved by the elastic spring mechanism.If the characteristics of swimming mechanism,muscular and elastic mechanism could be applied to biomimetic underwater robot,the robot would be more efficient,flexible and pressure-resistant.