This paper is about evaluating the minimum efficiency of hole cleaning and cuttings transport during drilling of vertical and deviated wells by a statistical-regression model using the Buckingham Pi theorem of dimensional analysis technique. The model will be evaluated by deriving the unknown proportionality constant and five exponents utilizing the statistical - regression curve of the least- squares fitting method and using the prepared field data from five drilled wells in the Gulf of Suez Company (GUPCO) fields. Then, the model's equation will be differentiated partially with respect to one of the independent parameters which are average annular velocity of drilling fluid, drilling rate of penetration, drill string rotation, drilling fluid density, yield point, plastic viscosity, density of drilled-cuttings, and coefficient related to hole deviation angle. Then it will be evaluated over a range of values for these parameters. From the parametric study, it is found that the hole cleaning efficiency increases as the average annular velocity, yield point, plastic viscosity, drill string rotation, density of drilling fluid increase. It is found also that efficiency decreases when drilling rate, cuttings density, hole deviation angle increase. Finally, it is recommended that the model can be applied in oil well drilling industry in different fields and horizontal wells rather than the vertical and deviated wells used in the paper.