The work in this paper concerns an analytical model for quantitatively describing the bending behaviour of aluminium profiles produced in a novel extrusion process: the differential velocity sideways extrusion (DVSE), in which two opposing rams with a velocity of v1
and v2
were employed, respectively. The analytical model was built on the basis of the upper bound theorem utilising a general streamline equation controlled by a shape factor n, and the curvature was calculated using the material flow velocity gradient across the die exit orifice. The predicted material flow velocity across the die exit orifice, and extrudate curvature agreed well with the finite element (FE) modelling results, which were found to be irrespective of the shape factor n of the streamline equation. For a given extrusion ratio, the minimum value of n = 2 leads to the minimum and closest theoretical extrusion pressure, the n value for obtaining the best approximated mean effective strain of the extruded profile increases with the increase of the velocity ratio v2/v1
, and the value of n = 3.5 gives the closest mean effective strain as a whole.