Abstract: Drilling fluid mostly behaves as non-Newtonian fluid and it can be modelled by the Herschel-Bulkley model, which is also called yield power-law (YPL). This model provides accurate results for a wide range of shear rate. In the present paper, a numerical study of the Herschel-Bulkley fluid through the eccentric annulus (E=0.5) was performed for the laminar flow regime using finite volume method (FVM). Effect of the inner pipe rotation and rheology parameters (yield stress τ₀, consistency index K and behavior index n) on the axial and tangential velocity profiles and pressure drop gradient were studied. Results showed that increasing the inner pipe rotation from 100 to 400 rpm induces an increase of 120 % of the maximum axial velocity. Low value of the behavior index (n=0.2) causes the appearance of the secondary flow in the wide region of the annulus. The variation of the inner pipe rotation and rheological parameters of the Herschel-Bulkley fluid have a negligible effect on the tangential velocity profile in the wide region of the eccentric annulus. Furthermore, It was observed that the increase of the inner pipe rotation from 0 rpm to 400 rpm causes a decrease of 10% of pressure drop gradient of yield power-law fluid for all eccentric annulus (E=0.2, E=0.4, E=0.6 and E=0.8).