A new type of viscometer is described, whose basic principle is the measurement of the damping of a fluid on a small resonant element. The major advantages of this instrument are that only small samples are required for analysis and that rapid cyclical measurements are possible. The viscometer can be used with Newtonian and non‐Newtonian fluids. In the present paper a theoretical analysis for a Newtonian fluid only is given. The theory is shown to predict the measured damping characteristics well for a number of test fluids.