The purpose of this Thesis is to research the literature of thrust allocation, thruster modelling and maneuvering design, as well as to design and simulate various dynamic thrust allocation algorithms. Vessels with dynamic positioning (DP) systems are high in demand in multiple industries due to their good abilities to keep position. An important component of the DP system is thrust allocation; algorithms which transform desired forces in surge, sway and yaw into thruster setpoints and rotation angles.Two dynamic thrust allocation algorithms are developed, and a simulation model of a model vessel is developed and used to test the thrust allocation algorithms. Findings indicate that the more complex the algorithms are, the more oscillatory the transients become. In addition, numerical instability is a significant concern because of the sensitivity of the barrier function used. Nonetheless, dynamic thrust allocation represents a powerful way to handle saturations.