The mechanical behavior of three styrenic thermoplastic block copolymer elastomers with applied surgical sutures was studied by uniaxial tensile testing. The materials exhibited oriented cylindrical microstructure. Distinct macroscopic deformation mechanisms have been observed upon stretching of samples with vertical and horizontal orientation. Deformation progressed along the axis of the suture in samples with parallel orientation (P), while it in case of normal orientation (N) the whole sample responded to the applied force. Also the analysis of the stress–strain curves showed a significant difference between samples P and N. Greater stress at break was observed for samples P, while samples N showed the capability to tolerate higher strain. The influence of morphology on the tear-out shape has been also observed. The thread made a vertical tear out in samples P while for samples N ripping off the bottom was observed.