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Using numerical simulation, we investigate the high-order plasmon resonances in individual nanostructures of an Ag nanorice core surrounded by an Al2O3 shell. The peak positions of localized surface plasmon resonances (LSPRs) are red-shifted exponentially with the increase of the dielectric shell thickness. This is due to the exponential decay of electromagnetic field intensity in the direction perpendicular to the interface. This exponential red-shift depends on the wavelength of the resonance peak instead of the resonance order. In addition, we find that the LSPRs in an Ag nanorice of 60-nm width can be perfectly described by a single linear function. These features make nanorice an ideal platform for sensing applications. [ABSTRACT FROM AUTHOR]