To simplify manufacturing and assembling work for a device without the technique of lapping an upper iron to a lower iron by forming the pressing surface of one iron by a mesh material, forming a cavity part at the back of the mesh material, and providing a support frame with a heating means.

In a mesh pressing apparatus, when an upper iron 1 is pressed to a lower iron 2, even if a mismatch in shape between the upper iron 1 and the lower iron 2 due to the fitting position of the upper iron 1 or inclination is caused, the pressing surface 3a formed by a mesh material 3 can be deformed according to the form of the lower iron 2, so that the pressing surface 3a comes into contact with the lower iron 2 on the whole area, and the pressurizing force is dispersed by tension applied to a line material for forming the mesh material 3, whereby contact will not be caused in a specified area of the surface of the lower iron 2. Accordingly, it is not necessary to provide strict lapping between the upper iron 1 and the lower iron 2, and formation of the pressing surface 3a of the upper iron 1, the fitting position of the upper iron 1 and the angle adjustment can be facilitated.