Theoretical predictions are presented for the operating characteristics of a quartz crystal microbalance (QCM) system consisting of the crystal, an attached viscoelastic sample layer, and a surrounding viscoelastic bath medium. Predictions are given for the spatial variation of "particle" velocity and velocity gradient throughout the sample layer, for the characteristic mechanical impedance acting on the crystal surface due to the viscoelastic sample layer plus surrounding bath medium, and for the resultant changes, Delta f(r), in the resonance frequency of the QCM. Errors introduced by employing the usual simple Sauerbrey-type Delta f(r)/sample-layer-mass relationship, together with a constant frequency offset to approximate the effect of the viscoelastic bath medium, are explored. In general, the viscoelastic properties of both the sample and bath media can substantially affect the apparent thickness (mass) of the sample layer if it is obtained by employing the typical Sauerbrey-type approximation noted above.