The present work describes a numerical and experimental investigation concerning the relative motion between purely viscous non-Newtonian fluids and spherical and cylindrical particles inside a tube. The influence of the rheological behavior of the fluid and the geometry of the particle on the parameters DeltaP(+)A/D (ratio between the additional force and the drag force acting over the particle) and F-W(+)/D (ratio between the additional force on the duct wall and the drag force acting over the particle) were investigated. Results are shown for the Reynolds number range between 0.008 and 2200, and for the power-law exponent of the fluid in the range from 0.1 to 2, and for the aspect ratio between the characteristic dimension of the particle and the duct in the range from 0.05 to 0.98. For all cases, and far beyond the Oseen's regime, the ratios DeltaP(+)A/D and F-W(+)/D can be directly evaluated by means of parameters of the undisturbed flow, which according to an existing theory, should only be expected for low Reynolds number. Suddenly, a strong transition occurs on the values of the ratios DeltaP(+)A/D and F-W(+)/D.