Hydraulic tortuosity is commonly used as an input to macroscopic flow models in porous media, accounting for the sinuosity of the streamlines. It is well known that hydraulic tortuosity does not depend on the applied pressure gradient for Newtonian creeping flows. Nevertheless, this is not necessarily the case for yield stress fluids flows, given the directional nature of both yielding and shear-thinning behaviour. This study aims at a breakthrough on the relationship between the hydraulic tortuosity and the level of yielding. To do so, the hydraulic tortuosity of the flow paths is evaluated in 2D porous media by means of direct numerical simulations and subsequently put in relation with the morphological information of the medium provided by pore-network modelling. Moreover, the effects of pore dimensions, spatial disorder and rheological parameters on yielding behaviour are examined. In most situations, the reported tortuosity values are lower than those obtained for Newtonian fluids.