Based on the special rheological model of foam fluid, the mathematical models of cuttings transport for stable foam drilling in vertical/near vertical sections, the transitional section, and inclined/horizontal sections are established in this paper. The effects of various flow parameters on the cuttings bed thickness in the annulus are analyzed. The results show that inclination, annulus velocity, foam flow rate, and eccentricity are key factors affecting cuttings transport. The thickness of a cuttings bed gradually decreases with the inclination decrease of the highly deviated/horizontal sections. When the inclination is reduced to approximately 60°, the dynamic and static cuttings bed disappears and is substituted by the glide lamella, which consists of cuttings grains. Cuttings grains have various forms of movement on the lower borehole wall. When the inclination is reduced to below 30°, the cuttings are brought out of the well by the stable foam if the returning velocity of the annulus foam is larger than the depositing velocity of the cuttings. The thickness of the cuttings bed gradually decreases with the increase of annulus velocity. The increased foam quality reduces the concentration of annulus cuttings when the annulus velocity is constant and when it reaches a stable status earlier than the foam drilling fluid of lower foam quality. However, the concentration of the annulus cuttings at the final stage is constant. The thickness of the cuttings bed increases with increased eccentricity of the drill stem. When the eccentricity is large, the change of eccentricity has a high effect on the cuttings bed thickness.