Swallowing sounds from cervical auscultation include information related to the swallowing function. Several studies have been conducted on the screening tests of dysphagia. The literature shows a significant difference between the characteristics of swallowing sounds obtained from different subjects (e.g., healthy and dysphagic subjects; young and old adults). These studies demonstrate the usefulness of swallowing sounds during dysphagic screening. However, the degree of classification for dysphagia based on swallowing sounds has not been thoroughly studied. In this study, we investigate the use of machine learning for classifying swallowing sounds into various types, such as normal swallowing or mild, moderate, and severe dysphagia. In particular, swallowing sounds were recorded from patients with dysphagia. Support vector machines (SVMs) were trained using some features extracted from the obtained swallowing sounds. Moreover, the accuracy of the classification of swallowing sounds using the trained SVMs was evaluated via cross-validation techniques. In the two-class scenario, wherein the swallowing sounds were divided into two categories (viz. normal and dysphagic subjects), the maximum F-measure was 78.9%. In the four-class scenario, where the swallowing sounds were divided into four categories (viz. normal subject, and mild, moderate, and severe dysphagic subjects), the F-measure values for the classes were 65.6%, 53.1%, 51.1%, and 37.1%, respectively.