In the last years the cost for rig rental has become very high. To reduce total cost it has been necessary to increase the cost efficiency when drilling to improve profit. One way to improve profit is to reduce the nonproductive time related to faults and failures which could occur during drilling. In addition many of the oil fields in the north sea are starting tail production where the pressure window are small which means that managed pressure drilling or under balanced drilling must be used. This thesis combines fault tolerant control and managed pressure drilling to see if it is feasible to continue drilling with fault in the system. The fault tolerant control system is based on model matching. Simulation is done of choke blocked in closed position such that back pressure pump is used to control the bottom hole pressure. Simulation is done with MATLAB. This to see if it is possible to use back pressure pump if the choke is blocked to such that drilling can proceed even if there is a choke failure which normally would result drilling stop. A simple hydraulic model is used in the simulation. The model does not apply actuator dynamics.The results where positive, back pressure can be used to control bottom hole pressure during managed pressure drilling. The results also showed that the transient between normal and fault system causes controller initiation problem which introduced bumps into the system.