This report presents the study of two-equation turbulence modeling. The primary objective of this study is to implement two-equation k-[epsilon] and k-[omega] turbulence models as a part of the incompressible flow solver, U2NCLE, on unstructured grids. There are several two-equation models but the selection of one which is in par with the model in UNCLE solver is required so that this model can be compared for robustness and accuracy as demonstrated by turbulence models in UNCLE. The selection also requires that the pre-defined arrays and variables can be used to avoid overhead and deviation from the solution procedure used in U2NCLE. The present study deals with the two-equation k-[epsilon] model contributed by Shih and Lumley and the two-equation k-[omega] model contributed by Wilcox. Implementation of these models will give the user multiple options of two-equation turbulence modeling for solution purpose. Particular attention is paid to the efficiency of the implementation. Various approximations to the source terms are considered and the most optimal and accurate approximation is identified. These models are validated via relatively small model problems, for example a flat plate case, by comparing the results with the results obtained from the respective models in UNCLE and the existing two-equation q-[omega] model in U2NCLE. Further validation is carried out by comparing computed forces and moments with experimental data for SUBOFF model with sail and stern appendages.