The present invention is directed to a system for thermoforming a batch of dental appliances simultaneously. An embodiment of the invention includes a vacuum plate having an upper surface and a plurality of cups for receiving dental models. A polymer sheet extends over the upper surface of the vacuum plate and over the cups. A heater cap that is movable in proximity to the cups is provided to heat the polymer sheet to be formed onto the dental models. The vacuum plate is configured to create a vacuum seal between an upper edge of the cups and the polymer sheet. A vacuum source is provided to apply a vacuum to the cups below the polymer sheet wherein the pressure contained in said cups is lower than atmospheric pressure whereby at least a portion of the polymer sheet is drawn into each of the cups and drawn over the dental models to form an aligner over each of the dental models. The invention includes the process of drawing a vacuum in a series of steps, or phases, to the cups below the polymer sheet to form the polymer effectively around the dental model.