Managed pressure drilling is a sophisticated pressure control method which is intended to meet increasingly high demands in drilling operations in the oil and gas industry. With this method, the well is pressurized and the drilling mud is released through a control choke which can be used to actively control/reject pressure variations. Such a control system needs to handle several disturbances, and in particular, vertical motion of the drill string causes severe pressure variations that need to be compensated by active use of the control choke. In this thesis we first analyze data from previous experiments with an existing control strategy and show that the main reason for the poor disturbance rejection is due to a control strategy based on an insufficient model of the pressure fluctuations, although practical issues like sampling time and choke friction also played a part. Then, we present several different control strategies for regulation of both top side and bottom hole pressures based on more detailed models of the well pressure dynamics. All controllers are tested in simulations and it is shown that either an output regulation controller or a controller based on the internal model principle will achieve satisfactory disturbance rejection. Lastly, some of these controllers are also tested on a high fidelity drilling simulator from IRIS, and a pressure regulation within plus/minus 0.5 bar is achieved for the choke pressure, and plus/minus 1.5 bar for the bottom hole pressure.