A method for production of a multi-layer gap-less steel pipe. An inner pipe and an outer pipe are formed from thermomechanically rolled steel strip with high notched bar impact strength by welding. The individual helical welding seam steel pipes of about the same lengths are matched with a difference of less than about one percent between the outer diameter of the inner pipe and the inner diameter of the outer pipe. The matched inner pipe is inserted into the outer pipe and the pipes are mechanically expanded with diameter control to a preset outer diameter of the multi-layer steel pipe. The resulting multi-layer steel pipe has the inner pipe disposed under compression and the outer pipe layer disposed under stress. The presence of a compression stress in the inner pipe provides a means opposed to hydrogen sulfide stress corrosion. The advantages of the helical welding seam steel pipes can be combined such as economic production, advantages relating to crack formation and crack propagation stopping, and the availability of high internal pressure loads upon use of thin, economic steel strip of different yield strength.