A material forming apparatus comprises: a support which is positioned at a side of a forming tool with respect to a material arranged on the forming tool to have a first part covered by the forming tool and a second part separated from the forming tool, and which supports the forming tool; a diaphragm which presses the second part of the material while the outer surface of the expanded diaphragm comes in close contact therewith, in a state in which the first part of the material is compressed by the forming tool and the outer surface of the diaphragm; and a volume-varying member which is disposed near the forming tool between the diaphragm and the support so that at least a portion thereof is positioned on the second part of the material.