This work evaluates the use of non-linear model predictive control (NMPC) for multivariate control of pressure and flow during underbalanced drilling (UBD) using a fit-for-purpose mechanistic model. Flow and pressure control are instrumental to the stability, safety, and successful drilling of a well. Failure to keep within the pressure envelope may have severe economic and environmental consequences. A relevant drilling scenario with different control objectives is evaluated to show the impact of the tuning and configuration of the control system. It is shown that with a sufficiently good model match, it is possible to achieve good performance with small deviations from the selected operational criteria, even when there are large changes in operational area. The multivariate control system manipulates choke pressure, pump flow, and separator set-points to simultaneously achieve both downhole and topside objectives. The optimization problem is solved within the relevant time dynamics of the system. (C) 2018 Elsevier Ltd. All rights reserved.