An OTEC CWP can be modelled as a submerged freehanging pipe conveying fluid. The large amount of the required transported deep seawater might cause catastrophic failure of the pipe due to Centrifugal and Coriolis forces driven by the Internal Flow Effect (IEF). To predict the critical velocity, this paper analyzes the stability of the pipe using a Finite Element Method. At the first step, the general motion equation of the pipe is derived and for each term of the equation, its potential energy equation is represented. Using Hermite shape functions, the local matrixes of each element can be obtained based on virtual displacement principle. Flow field and flow direction change at the inlet is considered at the bottom-end of the pipe as a local boundary condition. After the global matrixes of the system are produced, the global boundary conditions are imposed. Finally, the system is solved using the Newmark time-scheme method. The result are then compared to the previous published works of a small scale model. After being verified, the developed FEM will be used to analyze the full-scale model of the OTEC CWP. The result shows that the critical velocity is around 4.5-4.8 m/s.