The damping caused by polymer melt, which commonly gets into the housing of a shear stress transducer, is determined analytically. The analysis employs bipolar coordinates and is applied to Newtonian and then linear viscoelastic fluids, Results are compared with available dynamic calibration measurements, and also with previously used semi-empirical models for the transducer damping. Dimensionless graphs are then provided for estimating transducer attenuation and phase error in oscillatory shear measurements. Examples are given showing how to use the results for rheometer design and to assess measurement accuracy.