Origami-type cartons have been widely used in packaging industry because of their versatility, but there is a lack of systematic approach to study their folding behavior, which is a key issue in designing packaging machines in packaging industry. This paper addresses the fundamental issue by taking the geometric design and material property into consideration, and develops mathematical models to predict the folding characteristics of origami cartons. Three representative types of cartons, including tray cartons, gable cartons, and crash-lock cartons were selected, and the static equilibrium of folding process was developed based on their kinematic models in the frame work of screw theory. Subsequently, folding experiments of both single crease and origami carton samples were conducted. Mathematical models of carton folding were obtained by aggregating single crease's folding characteristics into the static equilibrium, and they showed good agreements with experiment results. Furthermore, the mathematical models were validated with folding experiments of one complete food packaging carton, which shows the overall approach has potential value in predicting carton's folding behavior with different material properties and geometric designs.