This paper examines the stability of a riser conveying fluid for Ocean Thermal Energy Conversion (OTEC) application by analytical and numerical approaches. Initially, the analytical solution for free hanging riser with fixed end connection is governed by including the components of the riser dynamics. Considering the boundary conditions, the general solution can be obtained using power series expansion. The imaginary and real parts of the solutions are plotted in an Argand diagram which is then used to predict the occurrence of instability. To verify the analytical solution, the dynamic behavior observed in the analytical solution is compared with the one predicted using numerical analysis. The numerical analysis here refers to a coupled analysis between riser and the fluid. After being verified, the analytical model is used to determine the acceptance of the proposed riser designs for 100 MW-Net OTEC power plant. In this paper, there are three materials being investigated which are steel, aluminum and FRP. For the given conditions, the results show that the critical velocity for steel-made riser is only about 0.9 m/s, for aluminum-made riser is about 1.7 m/s and the critical velocity for riser made of FRP is about 2.1 m/s.