In this thesis, a broader overview and description of foams is given. The first part provides a theoretical overview of foams. The second, practical part shows the construction of a CNC band saw machine for horizontal cutting of polymer foams. The emphasis is on polymer foams, and metal foams have been described to a shorter extent. Initially, the broader context of polymer foams is presented. The sequel brings the division and systematization of hollow or foam products and materials. The production of polymer foams is shown on a concrete example of the production of the most widely used polyurethane (PUR) and polystyrene (PS) foams. In order to get acquainted with the processes of production and machining of PUR foams, a visit to the company “Polimix d.o.o.” was made. The examples of PS and PUR foam applications the daily usage is shown. The application of some other, today very used foams is also presented. The following is a demonstration of the machining of polymer foams and the associated equipment and tools. The second, practical part describes the course of construction of the machine model step by step. “Solidworks” software was used. The knowledge of modeling using the software during the college has been upgraded with some new tools and command modules. The description is conceived precisely with an emphasis on them. The machine configuration consists of a movable work table and a fixed bridge. The result of the thesis is a model of a CNC band saw foam cutting machine.