Rheological properties of beverages contribute considerably to texture perception. When developing new beverages, it is important to have knowledge on the smallest differences of viscosity which a consumer can discriminate. Thickness is the sensory attribute most commonly used to describe the viscosity of beverages. The aim of this study was to determine the Just Noticeable Differences (JNDs) of oral thickness perception and the Weber fraction (K) of Newtonian model stimuli (maltodextrin solutions). JNDs were determined using the method of constant stimuli with 5 reference stimuli ranging in viscosity from 10 to 100 mPa·s. JNDs increased with increasing viscosity of the reference stimulus. The Weber fraction (K) for oral thickness perception of model beverages was K = 0.26 for the studied viscosity range. The Weber fraction for oral thickness perception is comparable to Weber fractions reported in literature for perception of kinesthetic food firmness and spreadability, creaminess, sourness, and bitterness perception. This demonstrates that the human sensitivity towards oral discrimination of thickness of liquid stimuli is comparable to the human sensitivity towards discrimination of specific texture properties and specific taste stimuli.