An elastic thread supply device 100 including a tension controller 130 configured to control the stress acting upon an elastic thread TH drawn from an elastic thread package P, and a drive roll 140 configured to supply the elastic thread TH dispensed from the tension controller 130 to a processing line 30. The drive roll 140 operates at a supply velocity v2 slower than a conveyance velocity v1 of a web W, and increases or decreases the supply velocity v2 depending on the fluctuation in the conveyance velocity v1.