A grid apparatus which has a multiplicity of ribbon-shaped grid elements stretched in tension and attached to a frame which comprises a pair of support bars and a pair of resilient support members. Metallic members which have a larger thermal expansion coefficient than the resilient support members are connected to the reverse surfaces of the resilient support members opposite the side to which the grid-elements are attached. In the grid apparatus during heat treatment, thermal creep of the grid elements is prevented so that the tension of the grid elements will remain high when the normal temperature state is resumed. A method of making such grid apparatus includes an additional heat treatment such as a blackening process after the reduction of the tension applied to the grid elements by the resilient support members and the support bars, hence preventing thermal creep of the grid elements to produce a high-reliability with high tension of the grid elements.