This work focuses on the application of a novel click chemistry approach, based on triazolinediones (TAD), to produce elastomeric membranes by electrospinning. TAD chemistry has been applied as a post-treatment to tune the mechanical properties of fibrous membranes consisting of styrene-butadiene-styrene (SBS) triblock copolymers. In addition, an eco-friendly SBS electrospinning solution was developed by electrospinning the SBS fibers from a butyl acetate solution to which LiBr and a bifunctional TAD molecule were added to increase the conductivity and the amount of polymer entanglements, respectively. Straightforward postmodification of these fibers was achieved by submerging the SBS membranes in a TAD-acetone solution. The use of, respectively, phenyl TAD or bifunctional TAD allowed for the introduction of phenyl groups as well as chemical cross-links and thus to tune the mechanical properties of the fibers, resulting in an elongation at break between 90 and 700% and a modulus from 100 to over 120 MPa.