Drilling fluids are complex materials that display elastoviscoplastic and thixotropic characteristics. Rotational viscometers that impose discrete rotational velocities, such as the Fann 35A, are traditionally employed to evaluate the rheological properties of drilling fluids in field operations due to their robustness and low cost. These viscometers are used to measure the steady-state shear stresses by imposing different shear rates and the transient stress overshoot as an estimation of the fluid's gel strength. In the current work, two synthetic drilling fluids and two bentonite suspensions were tested in a Fann 35A viscometer and in a rotational rheometer to check how accurate the Fann 35A viscometer results can be in comparison to rheometer data. Although the steady-state shear stresses measured by the Fann 35A were corroborated by the corresponding values obtained from the rheometer, the accuracy of Fann 35A on measuring the stress overshoots depends on the fluid rheological characteristics. Two hypotheses were proposed to explain the difference on the stress overshoots: (i) wall slip and (ii) the inappropriate control of the shear rate.