Paclitaxel (PTX) is a natural terpenoid compound that has been broadly studied for its antitumor activities and widely used as a chemotherapy medication. The treatment efficacy of PTX is affected by its low aqueous solubility, thus causing a subject of extensive research. In recent years, synthetic molecular containers such as cucurbit[n]urils (CB[n]s) and their derivatives have been significantly developing because of their remarkable ability to bind hydrophobic and cationic drugs. Recent experimental studies have shown that acyclic CB[n]-type containers (aCB[n]s), as new derivatives of the family of CB[n]s, increase the solubility of insoluble pharmaceuticals. However, the nature by which the drug interacts with carriers remains largely unknown. In this study, molecular docking and molecular dynamics (MD) simulation were performed to understand how CB and aCB nanocontainers interact with PTX which affect its aqueous solubility. The results clarify how the flexibility of containers is influenced by their structure and how this affects their interactions with PTX. Our results reveal that although both CB and aCB are capable of binding to PTX, the affinity to aCB is higher than that of CB. It has also been shown that the binding to both CB and aCB is probably an entropy-driven process. This research supports the potential use of the cucurbit[n]urils and their acyclic derivatives as drug delivery systems.