Basic understanding of the means by which multidrug efflux systems can efficiently recognize and transport drugs constitutes a fundamental step toward development of compounds able to tackle the continuous outbreak of new bacterial strains resistant to traditional antibiotics. We applied a series of computational techniques, from molecular docking to molecular dynamics simulations and free energy estimate methods, to determine the differences in the binding properties of imipenem and meropenem, two potent antibiotics of the carbapenem family, to MexB, the RND transporter of the major efflux system of Pseudomonas aeruginosa. We identified and characterized two affinity sites in the periplasmic domain of the transporter, sharing strong similarities with the distal and proximal binding pockets identified in AcrB, the homologue of MexB in Escherichia coli. According to our results, meropenem has a higher affinity to the distal binding pocket than imipenem while both compounds are weakly bound to the proximal pocket. This different behavior is mainly due to the hydration properties of the nonpharmacophore part of the two compounds, being that of imipenem less bulky and hydrophobic. Our data provide for the first time a rationale at molecular level for the experimental evidence indicating meropenem as a compound strongly affected by MexB contrary to imipenem, which is apparently poorly transported by the same pump.