In oil and gas well drilling operations, it is of great significance to accurately predict the drag coefficient and settling velocity of drill cuttings in non-Newtonian drilling fluids. In this paper, the free-falling of 172 groups of spheres and 522 groups of irregular-shaped sand particles in Newtonian/non-Newtonian fluids were investigated experimentally. It was found that the drag coefficient calculated based on Newtonian correlations can result in a significant error when the particle settles in the non-Newtonian fluid. Therefore, predictive models of drag coefficient were established respectively for different types of fluids. The validity of the proposed drag coefficient model of spheres was verified by comparing it with the previous works. On this basis, the drag coefficient model of irregular-shaped sand particles was established by introducing a shape factor. The models do not use the shape factor that requires detailed three-dimensional shape and size information. Instead, two-dimensional geometric information (circularity) is obtained via image analysis techniques. The present new models predict the settling velocity of sand particles in the power-law fluid and Herschel–Bulkley fluid accurately with a mean relative error of 5.03% and 6.74%, respectively, which verifies the accuracy of the model.