The hydrodynamic force acting on a rigid cylindrical particle moving with a constant velocity in an infinite shear-thinning fluid, which is simulated by a Carreau model, which is characterized by four parameter, the viscosity corresponding to the minimum shear rate, η0, the viscosity corresponding to the maximum shear rate, η∞ the relaxation time constantλ, and a measure for the rate of decrease in apparent viscosity as shear rate increases, n, is evaluated. The influences of the key parameters of the system under consideration on the behavior of a particle, including the relaxation time constant