This paper presents the results of an experimental study on the behavior of concrete confined by fiber reinforced polymer (FRP) jackets with a large rupture strain (LRS). The FRP composites considered herein are formed by embedding polyethylene naphthalate (PEN) and polyethylene terephthalate (PET) fibers in a suitable epoxy resin matrix. The PEN and PET fibers are usually made from recycled materials (e.g., PET bottles) and have a strain capacity greater than 5%. They are ideal for use in seismic retrofit applications where increases in ductility and energy absorption capacity are of prime concern. The present study has two specific objectives: (1) to develop a good understanding of the compressive stress-strain behavior of concrete confined with LRS FRP; and (2) to examine whether existing confinement models developed for conventional FRPs are applicable to LRS FRPs. As the existing models have been developed and verified mainly based on test data for CFRP and GFRP, which have a jacket hoop rupture strain of less than 2%, their accuracy in the hoop/lateral strain range beyond 2% is unclear. Results presented in this paper indicate that the two LRS FRPs made from PEN and PET fibers possess a bilinear tensile stress-strain relationship, which has a significant effect on the axial compressive stress-strain behavior of FRP-confined concrete. A recent confinement model for conventional FRPs is compared with the present test results, indicating that the model significantly overestimates the ultimate axial strain. A modified version of the model is then presented to provide more accurate predictions of the test results.