A system for levitating a softened, viscous or viscoelastic material by near field acoustic levitation. The system includes a support structure having a rigid surface, and a vibration generator operatively connected to the rigid surface. The vibration generator transmits acoustic waves to the rigid surface at a frequency and an amplitude sufficient to vibrate the rigid surface and create a gas squeeze film between the material and the rigid surface. The gas squeeze film has a pressure greater than ambient air pressure and sufficient to levitate the material. The system is particularly suited for transporting, forming, or casting heated glass. Also disclosed are methods for transporting, forming, and casting heated glass using near field acoustic levitation.