There has been much debate in recent years as to the effectiveness of enhancing heat and mass transfer rates with resonant acoustic oscillations in industrial equipment such as boilers, dryers, calciners, gasifiers, and others. This article will briefly discuss the theoretical background of acoustic drying, the setup of the experimental apparatus used to investigate the feasibility of acoustically enhanced drying, the results of these experiments, and, finally, some conclusions drawn from this work. The theoretical discussion focuses on the use of the quasi-steady assumption to estimate the potential for enhancing the heat and mass transfer rate to and from the material using acoustic oscillations. The experimental work reported focuses on the successful application of acoustical oscillations to drying a cellulose sponge, which is a material that readily transports moisture to its surface where it can be effectively dried. Also reported is the unsuccessful application of acoustic oscillations to the drying of polyethylene terephthalate, which is a saturated, thermoplastic, polyester resin made by condensing ethylene glycol and terephthalic acid and is commonly used in the manufacture of plastic food and drink containers. Reasons for success and failure in each case are discussed along with the implications of these to the successful application of acoustic oscillations to future drying applications.