A numerical model is developed for a TLP configuration of a floating offshore wind turbine. The platform dynamics and hydrodynamic forces are derived and implemented in an advanced aero-elastic code, Flex5, to compute the hydro-aero-servo-elastic loads and responses on the floater and the wind turbine. This is achieved through three steps. In the first step, an independent 2D code with fourteen degrees of freedom (DOFs) is developed and the responses are verified for load cases concerning steady and spatially coherent turbulent wind with regular and irregular waves. In the second step, the 2D code is augmented with three more DOFs. A three-dimensional wave model with directional spreading is derived and implemented to obtain 3D code. Comparison of the 3D responses with that of the 2D shows a good agreement. The 3D code is tested for load cases using steady and turbulent wind with 3D irregular waves. In addition, the effect of wind-wave misalignment is investigated. Further, in the third step, the 3D platform dynamics and wave loading are implemented into Flex5, resulting in a fully coupled hydro-aero-servo-elastic code. The implementation is tested to make the model reliable and robust. In addition, the responses are compared to that of the 3D code responses, which shows a good agreement, in general. The extended Flex5 code is used to carry out a parametric study to investigate the influence of various configurations on the responses when subjected to different sea states and a potential configuration is recommended. The potential configuration is subjected to sea states with more narrow wave spectrum with collinear and oblique wave heading and a swell case. The responses are compared with that of the baseline configuration and recommendations are suggested for future work.