The impact of oil spills on the environment and the economy of a region motivate governments to improve their preparedness in dealing with spills to mitigate the damage. The vector-based oil spill models presented here can serve as a basis for future models for the islands of Trinidad and Tobago and the South Caribbean Sea. Two models, surface and depth, are developed using a Lagrange Element method and the results are examined. The output from the Surface Model performs favorably when compared to an actual spill. However, the inclusion of additional variables into both models would improve the accuracy of the spill trajectories. It is concluded that the Surface Model developed in this study can be applied to actual hydrocarbon spills, producing a more effective approach to the combat method and reducing its impact on the marine environment.