This invention provides a conveying apparatus and a blasting machine equipped with the conveying apparatus that can prevent workpieces from being damaged by the used abrasives attached to the conveying rollers.For the conveying apparatus, a peripheral part 33a disposed at the peripheral surface of a rolling member 33 of a rolling roller 31 is made of a softer elastic material than the material of the panel P, wherein when used abrasives get stuck between the peripheral part 33a of the rolling member 33 and the panel P, since the peripheral part 33a acts as a cushioning material that can reduce the force caused by the used abrasives and loaded on the panel P, even if the panel P is made of a fragile material, such as glass, the panel P can be conveyed without flaws being caused by the used abrasives.