A series of polymeric orthodontic appliances is made by providing a set of tooth analogs, each having a model crown that represents the shape of a corresponding tooth of the patient. The tooth analogs are moved along respective guides as needed in order to bring the associated model crown an incremental step toward or away from its desired position. The polymeric appliance is formed by placing a sheet of polymeric material over the model crowns after at least one tooth analog has been moved to create a desired model tooth arrangement.