Additive manufacturing is an advanced manufacturing technology that allows building any complex 3D geometry of product by adding layer by layer of material. One of the most important effectiveness of additive manufacturing is able to manufacture lattice structure inside product space in order to reduce the usage of material and the weight of the product but still ensure its mechanical properties. The lattice structure is a network of bars linked each other in a space of product and it can be quickly manufactured due to the development of additive manufacturing technologies. However, the design of a model of the lattice structure in the computer-aided design environment has many difficulties. The current modeling technologies do not support product designer to automatically create a model of the lattice structure with the different type of configurations. Therefore, the paper will present new approaches to automatically generate a 3D model of the lattice structure in the design space of the product. These approaches allow creating different configurations of the periodic or non-periodic lattice structure.