Recently, a new stability criterion has been introduced for general cylindrically symmetric thin-shell wormholes. The present work deals with thin-shell wormholes in the background of static cylindrically symmetric space-time i) with a cosmological constant and ii) with or without a magnetic field in Brans-Dicke gravity and the stability criterion is examined in the perspective of this newly introduced stability analysis. Finally, the stability conditions have been analyzed geometrically. © 2018, Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature.