Non-Newtonian flows are of great scientific interest due to their distinctive rheological behaviour. Free-surface non-Newtonian flows are encountered in many environmental and industrial applications, such as mud flows and moulding flows. Smoothed particle hydrodynamics (SPH) is an excellent technique for describing free-surface flows, but traditionally suffers from an inaccurate pressure field. The diffusion-based incompressible SPH (ISPH) method which was first introduced by Lind et al. (2012), following the original shifting methodology of Xu et al. (2009), combines the benefits of the SPH methodology with a virtually noise-free pressure field. In this work the diffusion-based ISPH method is extended to solve inelastic non-Newtonian flows, introducing standard viscosity calculation techniques for the non-Newtonian fluids and adopting a new viscous term which is more suitable for the calculation of such flows. The new approach is validated against internal flows and free-surface flows by comparing with analytical and experimental results respectively. Furthermore, comparisons with other computational techniques were conducted and showed that in addition to the accurate prediction of free-surface flows, the proposed methodology can significantly improve the prediction of the pressure field. (C) 2015 Elsevier B.V. All rights reserved.