Water- and oil-based drilling fluids are polydisperse non-Newtonian systems, the stress state of which is adequately described by the Herschel – Bulkley rheological model. This study hypothesizes that cuttings transport efficiency can be improved by selecting the most effective combination of the three parameters of the rheological model – yield stress, consistency index, and flow behavior index – when designing drilling fluid properties. The effective parameter combination of the Herschel – Bulkley model for achieving a uniform velocity profile was determined using correlation and regression analysis methods as well as machine learning techniques. The computational part of the work was performed in the Wolfram Mathematica symbolic calculation package. Deterministic regions of the dependence of the velocity profile uniformity index on the rheological coefficients were identified. For practical engineering calculations, a linear mathematical model was constructed to represent the relationship between the modified excess coefficient and the parameters of the three-parameter Herschel – Bulkley rheological equation. The proposed methodology can be recommended for designing new drilling fluid systems and testing existing ones under given wellbore cleaning conditions.