This paper proposes a non-invasive, acoustic-based method to differentiate between individuals with and without dysphagia or swallowing dysfunction. Swallowing sound signals, both normal and abnormal (i.e., at risk of some degree of dysphagia) were recorded with an accelerometer over the trachea. Segmentation based on waveform dimension trajectory (WDT, a distance-based technique) was developed to segment the non-stationary swallowing sound signals. Two characteristic sections emerged, Opening and Transmission, and 24 characteristic features were extracted and subsequently reduced via discriminant analysis. A discriminant algorithm was also employed for classification, with the system trained and tested using the leave-one-out approach. Overall, 350 signals were used from three bolus consistencies (semisolid, thick and thin liquids). A final screening algorithm correctly classified 13 of 15 control subjects and 11 of 11 subjects with some degree of dysphagia and/or neurological impairments. The proposed method has great potential to reduce the need for videofluoroscopic swallowing studies (the current gold standard method for swallowing assessment, which is invasive and non-portable) and the overall clinical assessment of swallowing sound signals.