A dental flossing device is made of an elastic material. Its central structure is a flexible, elastic, bridge strip with a cross section having different shapes. When stretched, the strip has a changeable diameter to help remove debris between teeth. The strip includes corrugations or spirals along its length and may include different drugs or flavors to give the user a medicine or a taste while cleaning the teeth. At each end of the strip, there is an elastic opposing handle. Each device is stored in a carrying case for easy removal before use. A method for making the dental flossing device out of the elastic material includes molding the elastic, flexible, bridge strip and integrally molding the elastic opposing handles at opposite ends of the strip.