The large-scale and uncoordinated integration of distributed photovoltaic (DPV) systems has introduced issues such as overvoltage and reverse power flow in distribution networks in mountainous areas, adversely affecting their stable operation. Accurately determining the DPV hosting capacity of distribution networks in mountainous areas has therefore become an urgent research problem. To address this issue, a deterministic model is constructed with the objective of maximizing the DPV capacity that can be accommodated by a mountainous distribution network, while explicitly considering the capacity health degradation of energy storage systems (ESS) and smart soft open points integrated with energy storage (E-SOP). Subsequently, DPV output characteristics are analyzed, and on the basis of the deterministic model, a two-layer robust model for DPV hosting capacity evaluation in flexible distribution networks in mountainous areas is developed. Then, the model is transformed into a mixed-integer linear programming problem using the KKT conditions and solved with the Gurobi optimizer. Finally, case studies are conducted on an improved IEEE 33-node flexible distribution network in a mountainous area to investigate the impact of ESS capacity health degradation and DPV output uncertainty on DPV hosting capacity. The results show that the proposed model increases DPV hosting capacity by 8.43%, demonstrating its feasibility and effectiveness.