The sensitivity and optical properties of silver nanoprisms (triangular plates with round-truncated corners) are investigated in this paper. Results of boundary element method simulations are compared with experimental results and literature data. Based on electron microscopy images of the synthesized nanoprisms, a single-particle model is set up for simulations with three running parameters: edge length, thickness, and roundness (defined as the radius of the circumscribed circle divided by the edge length). These geometric parameters can be optimized during chemical synthesis to create sensors with improved sensitivity. The effect of biomolecular layers is also investigated. As a novel approach to improve the agreement between the simulated and experimentally measured extinction spectra, the single-particle model is extended to consider the variation of the prisms’ parameters in the form of distributions. The resulting extinction cross-section spectra correspond well with the experimental data. The calculated bulk refractive index sensitivity is 670 nm/RIU (RIU stands for refractive index unit) for the single particle model (length = 150 nm, thickness = 10 nm, and roundness = 0.1), while (690 ± 5) nm/RIU for the extended model. The presented model and obtained relations between sensitivity and geometry can be effectively used to design and optimize the fabrication technologies for silver nanoprism-based sensing applications.