Dynamic curved interfaces are fundamental and ubiquitous structures in biological systems. However, replicating the structure and function associated with these interfaces for mechanobiology and drug screening is challenging. Here, we develop a dynamic curvature-enabled microfluidic organ chip of two fluid-solid dynamic curved interfaces. One interface effectively integrates adjustable biomechanics, and the other controls drug release with open microfluidics. The fluid-solid interface sensed by the cells can modulate the residual stress, stiffness, strain of the solid phase, and the flow shear stress of the fluid phase. Using the chip, we investigate the mechanotransductive responses of endothelial and epithelial cells, including Piezo1, Ca2+, and YAP, and reveal that the response of the endothelium to combined dynamic cyclic strain and flow shear stress is different from separate stimulation and also disparate from the epithelium. Furthermore, direct and high-efficiency drug release to cells is realized by constructing the other fluid-solid interface on the back side of cells, where drugs are encapsulated within cross-linked alginate hydrogel in the open microfluidic channel. Then, we replicate object-specific and location-specific biomechanical environments within carotid bifurcation and prove the effectiveness of drug delivery. Our design exemplifies dynamic curved biological interfaces with controlled mechanical environments and holds potential for patient-specific medicine.