The formation of a cutting bed in an annulus involves safety problems in drilling especially in the horizontal well and the directional well. In this work, three axial laminar velocity field calculation models for the power-law fluid in an annulus are modified by considering the effect of the cutting bed. The proposed models are employed to numerically simulate the annulus flow with the cutting bed. Verified by the experimental data in literature, all of them can be applied to the situation of the annulus flow with the cutting bed. The modified concentric annulus model enjoys the best performance, while the flat channel flow model has the worst performance.