A coupling system for a structure accelerating through a fluid is considered which is composed of the structure and the fluid in a finite surrounding volume. Based on the variational principle, the finite element equations of hydrodynamic pressure and structural elastic vibration are deduced. A numerical method is given for the dynamic character and response of the structure which takes the coupled fluid into account. The effect of axial inertial forces on the dynamic character and response of rapidly accelerating structures is also considered.