Apparent and plastic viscosities are two of the significant rheological properties of drilling fluid. Monitoring the apparent and plastic viscosities during drilling operations is essential to prevent various drilling problems and achieve successful drilling operations. Due to the constraints associated with experimental measurements, a reliable prediction is regarded as an excellent alternative for quick assessment of the apparent and plastic viscosities. There were many attempts taken to develop models to predict the apparent and plastic viscosities. However, the published models' main problems are their lack of accuracy and limitation of the parameters included. Therefore, this work presents new statistical-based empirical correlations for the prediction of apparent and plastic viscosities. The developed correlations relate the apparent viscosity and plastic viscosity to some variables, viz. bentonite, nanoclay concentration, nanosilica concentration, and temperature. Published data were utilized, and Response Surface Methodology (RSM) was used to obtain the mathematical relation between the variables and responses and describe the variables' interactions. ANOVA then validated the correlations, F-statistics test, fit statistics, and Pareto chart standardised effects. The validation has shown that the RSM models were more robust with high accuracy. The influence of the independent variables on the apparent and plastic viscosities of the drilling fluids was established in response surface plots (3D), and the interaction between variables in the system was found statistically significant. The results show that the RSM model's performance is accurate, reliable, and can, hence, be used for precise prediction of apparent and plastic viscosities. © 2021 Elsevier B.V.