Flexible solar cells have a transformative potential for niche applications, but they face fundamental challenges in simultaneously achieving high-power conversion efficiency (PCE), extreme mechanical resilience and operational stability1–4. Here we demonstrate a certified 33.6%-efficient flexible perovskite/crystalline silicon (c-Si) tandem solar cell with a record open-circuit voltage (Voc) of 2.015 V, rivalling its rigid counterpart. The flexible tandem retains 91% of its initial PCE after 5,000 cycles under a bending radius (Rb) of 17.6 mm and demonstrates exceptional operational and damp-heat stability, featuring a T80 lifetime exceeding 2,000 h under continuous illumination and retaining 90% of its initial PCE after a 1,000 h damp-heat test. This advancement is enabled by the implementation of the reactive-plasma-deposited (RPD) cerium and hydrogen co-doped indium oxide (ICO:H) recombination layer that promotes self-assembled monolayers (SAMs) coverage and interfacial charge transfer, and in situ annealed zinc-doped indium oxide (IZO) front transparent electrode with markedly enhanced optoelectronic and mechanical properties.