Softness and firmness are seemingly incompatible traits that synergize to create the unique soft-yet-firm tactility of living tissues pursued in soft robotics, wearable electronics, and plastic surgery. This dichotomy is particularly pronounced in tissues such as fat that are known to be both ultrasoft and ultrafirm. However, synthetically replicating this mechanical response remains elusive since ubiquitously employed soft gels are unable to concurrently reproduce tissue firmness. We have addressed the tissue challenge through the self-assembly of linear-bottlebrush-linear (LBL) block copolymers into thermoplastic elastomers. This hybrid molecular architecture delivers a hierarchical network organization with a cascade of deformation mechanisms responsible for initially low moduli followed by intense strain-stiffening. By bridging the firmness gap between gels and tissues, we have replicated the mechanics of fat, fetal membrane, spinal cord, and brain tissues. These solvent-free, nonleachable, and tissue-mimetic elastomers also show enhanced biocompatibility as demonstrated by cell proliferation studies, all of which are vital for the safety and longevity of future biomedical devices.Copyright © 2020 American Chemical Society.