Spectral/hp element methods and an arbitrary Lagrangian–Eulerian (ALE) moving-boundary technique are used to investigate planar Newtonian extrudate swell. Newtonian extrudate swell arises when viscous liquids exit long die slits. The problem is characterised by a stress singularity at the end of the slit which is inherently difficult to capture and strongly influences the predicted swelling of the fluid. The impact of inertia (0⩽Re⩽100) and slip along the die wall on the free surface profile and the velocity and pressure values in the domain and around the singularity are investigated. The high order method is shown to provide high resolution of the steep pressure profile at the singularity. The swelling ratio and exit pressure loss are compared with existing results in the literature and the ability of high-order methods to capture these values using significantly fewer degrees of freedom is demonstrated.