The invention provides a slidably-stretched roof sheathing support device which comprises a support frame and a support framework fixed over the support frame in a supported mode. The upper end of the support frame is provided with at least one clamping tooth, the bottom of the support framework is provided with clamping feet corresponding to the clamping teeth, and the clamping feet are bucked in the clamping teeth in a clamped mode and can slide in the clamping teeth. According to the slidably-telescopic roof sheathing support device, the support framework is connected with the support frame in a slidably-stretched mode, the problems of temperature deformation and temperature stress cannot be generated during thermal expansion and cold contraction, and therefore the problems of roof sheathing arching, water leaking, service life shortening and the like which are caused by too large temperature stress are avoided.