Tuned Liquid Dampers (TLDs) are crucial for mitigating undesired vibrations in tall structures and high-rise buildings. Typically, a TLD consists of a rigid tank housing a shallow fluid, with the oscillation of the fluid, known as sloshing, responsible for dissipating the energy of the host structure. It represents a passive vibration control system. The modelling and design of TLDs are imperative prior to implementation in a host structure, achievable through either numerical simulations or physical experiments. While various analytical and numerical models have been proposed by researchers, analytical models often fall short in accurately capturing sloshing dynamics. In this research work, numerical models of partially filled rectangular and cylindrical TLDs developed through the Computational Fluid Dynamics (CFD) approach are presented. The models are implemented in COMSOL Multiphysics (version 6.0) software, addressing the sloshing phenomenon to provide a comprehensive understanding of damping behaviour. The model incorporates TLDs attached to a flexible host structure, achieved through the coupling of the Structural Mechanics and Computational Fluid Dynamics (CFD) modules present in COMSOL Multiphysics software. This numerical approach ensures a detailed and accurate representation of the sloshing dynamics, enhancing the reliability of TLD design for effective vibration control. Understanding the influence of shape and size of tanks is necessary for selecting the optimal configuration for specific applications enhancing overall functionality of TLDs.