Abstract: The flexible pipe for deep sea mining is the umbilical cord of transport which links mine-collecting machine and relcy buffer . The discrete finite element method . is the widely used technique to study the flexible pipe despite many assumptions with limitations . To overcome thedeficiencies of the discrete finite element method, a mathematical model is proposed . The three dimensional unsteady continuous partial differential equations of the model are presented, which take into accoun the nonlinear large displacement and the effects of transverse shears. It is shown that the mathematic model is applicable to the static or dynamic analyais of any slender structures with circular cross-section .