Quasi-static tensile and stress relaxation experiments were performed on several cloth-based and segmented elastomeric tapes, and the results were analyzed using viscoelastic models. The cloth tape modulus of elasticity was ∼340 MPa, while those of the kinesio tapes ranged from ∼15 to 20 MPa. The cloth tapes was also stronger and more brittle. Viscoelastic modeling of the stress relaxation behavior was done using a Zener model for the cloth tapes and a 5-element model for the kinesio tapes. The cloth tape relaxed by ∼20%, while the kinesio tapes relaxed by ∼40% of the applied maximum stress in approximately 300-s as demonstrated by viscoelastic modeling and constant strain experiments. The overall amount of long-term compressive force delivered by kinesio tapes might be inadequate for some applications, but they are more forgiving in how they are deployed.