Accurate and timely protein degradation is a vital cellular process. Protein degradation is performed by the 26S proteasome complex, a large multi-subunit molecular machine that recognizes, binds, and degrades protein substrates covalently bound to poly-ubiquitin tags. The 26S proteasome, which recognizes ubiquitin tags through its subunit Rpn10, has a preference for binding K48-linked tetra-ubiquitin chains. However, Rpn10 and its homologs usually have only one or two ubiquitin binding sites, located on their long and flexible C-terminal arms. Here, to examine the role of Rpn10 in the 26S proteasome preference for tetra-ubiquitin tags, we perform molecular dynamics simulations of Rpn10 bound to mono-ubiquitin and poly-ubiquitin chains. To overcome timescale and sampling limitations, we use a combination of a hybrid model force field (PACE) and temperature replica exchange molecular dynamics (T-REMD) simulations. The performed simulations characterize in detail Rpn10 binding to its ubiquitin partners and identify transient contacts that could stabilize Rpn10 (and 26S proteasome) binding to poly-ubiquitin chains. Our results demonstrate at atomic resolution how the flexible Rpn10 subunit contributes to the recognition of poly-ubiquitin tags.