Summary: Let \(Q_n\) denote the \(n\)-dimensional hypercube and the set of faulty edges and faulty vertices in \(Q_n\) be denoted by \(F_e\) and \(F_v\), respectively. In this paper, we investigate \(Q_n\) \((n \geq 3)\) with \(| F_e | + | F_v | \leq n - 3\) faulty elements, and demonstrate that there are two fault-free vertex-disjoint paths \(P [a, b]\) and \(P [c, d]\) satisfying that \(2 \leq \ell(P [a, b]) + \ell(P [c, d]) \leq 2^n - 2 | F_v | - 2\), where \(2 |(\ell(P [a, b]) + \ell(P [c, d]))\), \((a, b),(c, d) \in E(Q_n)\). The contribution of this paper is: (1) we can quickly obtain the interesting result that \(Q_n - F_e\) is bipancyclic, where \(| F_e | \leq n - 2\) and \(n \geq 3\); (2) this result is a complement to X.-B. Chen’s part result [Inf. Sci. 179, No. 18, 3110–3115 (2009; Zbl 1193.68050)] in that our result shows that there are all kinds of two disjoint-free \((S, T)\)-paths which contain \(4, 6, 8, \ldots, 2^n - 2 | F_v |\) vertices respectively in \(Q_n\) when \(S = \{a, c \}, T = \{b, d \}\), and \((a, b),(c, d) \in E(Q_n)\). Our result is optimal with respect to the number of fault-tolerant elements.