Surface plasmon represents oscillations of electrons at the interface between metal and dielectric layers. Surface plasmon resonance (SPR) is influenced by the environment near the surface, which has been the basis for label-free biosensor structure for various applications of molecular detection. An important aspect of SPR biosensing is that its characteristics are affected by the geometrical structure. Yet most research has focused largely on a structure using flat surface. Although flat structure is suitable for typical sensor applications, it may not be appropriate for wearable or in vivo applications. In this study, we analyzed the effects of surface curvature on flexible SPR biosensors. Curved surface was approximated using a segmented model in which each segment is treated as a flat surface with a different incident angle and then optical characteristics of the overall model were calculated by rigorous coupled wave analysis in two different configurations of light incidence. We calculated curvature effects on SPR with curvature radius larger than 255 μm. It was found that regardless of the incident configurations, resonance curves tend to broaden with increased curvature due to larger momentum dispersion. Resonance shifts as a result of DNA immobilization and hybridization decrease with curvature. The analysis was extended to multi-curvature structure and finds significant fluctuation of resonance shift for parallel light incidence. The study can be of profound importance for plasmonic devices using flexible substrates.