In this paper, the underwater vehicle, sling and the mother ship are c
onsidered as a single degree of freedom system connected by a spring.
Through the analysis of this system, a physical model is established,
which describes the motion of the vehicle caused by the ship motion an
d wave motion. Furthermore, a mathematical model based on this physica
l model is obtained, and a numerical solution program is made. As an e
xample, a practical launch and recovery system fbr an underwater robot
is calculated by use of the program, and the motion track of the robo
t is obtained.