In this study, a Finite Element Model (FEM) was developed to analyse the stability of an Ocean Thermal Energy Conversion (OTEC) Cold Water Pipe (CWP). The general equation describing the pipe dynamics was adapted from a previous study and modified to consider the non-linear drag force. The flow field and change in the flow direction were imposed by varying the coefficient of the centrifugal force to 0, 0.5, and 1. The pipe material properties were varied using GFRP, PE, ABS, and HDPE. Pipe length was varied from 600 to 1000 m with a 100 m increment. Initially, the analysis was performed in the frequency domain, yielding Eigen frequencies in complex numbers. Subsequently, the analysis was conducted in the time domain using the Newmark time-scheme method to produce dynamic responses for each time increment. The critical fluid velocities obtained from the frequency-domain analysis were verified in the time domain. The results showed that the critical velocities obtained from the frequency- and time-domain analyses were in good agreement. The critical velocity in the fixed configuration was slightly higher than that in the pinned joint by approximately 3%–5%. The existence of the centrifugal force strongly influenced the critical velocity, depending on the observed modes. We found that GFRP is the most suitable material for the OTEC CWP.