To provide vibration isolating support structure of a heat shield board which is capable of reducing influence in vibration of a fastening bolt of the heat shield board, in particular, influence in vibration in the radial direction of the bolt.

In the vibration isolating support structure of the heat shield board which supports the heat shield board (12) to an exhaust tube (11) of an engine, the structure is provided with a vibration isolating plate (16) forming an insertion hole (17), the heat shield (12) attaching the vibration isolating plate and an attaching screw (13) which movably attaches the heat shield board to the exhaust tube by inserting through the insertion hole of the vibration isolating plate. The vibration isolating plate is disposed on inner peripheral side of a hollow plate (16) including a hollow portion and contains a plurality of elastic bodies (16a-16d) which form outer edge of the insert-through hole. Each of the elastic bodies produces elastic force in diametrical direction of the hole of at least insertion hole (17).