Patented recently is a process of preparing an elastic thermally bonded nonwoven web, whereby the process is characterized by the following steps: (i) providing a thermally bonded nonwoven precursor web containing thermoplastic fibers, (ii) subjecting the precursor web of step (i) to a drawing treatment in a machine direction at a drawing rate of from 45 to 70%, and a strain rate within a range of from 1000 to 2400%/min at a temperature between the softening point and the melting point of the fibers for preparing the elastic thermally bonded nonwoven web.