Spreading of liquids and soft solids on a rigid surface in a surrounding liquid medium is investigated by utilizing the lateral sensitivity of the quartz crystal microbalance (QCM). While the QCM has been used extensively to study systems with spatial variations in the direction normal to the crystal's electrodes, few studies have exploited the QCM's ability to sense changes in loading in the plane of the electrodes. We propose equations to describe the predicted response of the QCM to a generalized viscoelastic material spreading at the QCM surface at the expense of the surrounding liquid medium. Several experimental examples are given in order to support the validity of the proposed equations, including situations where the spreading material is a Newtonian liquid, a viscoelastic liquid, or one of two viscoelastic solids. The first viscoelastic solid is a physically cross-linked gel based on a styrene/ethylene-butene/styrene triblock copolymer in mineral oil, and the second is a cross-linked poly(ethylene glycol) hydrogel.