High-resolution reconstruction of steeply dipping structures is an important but challenging subject in seismic exploration. Prismatic reflections that contain information on these structures are helpful for reconstructing steeply dipping structures. Elastic full-waveform inversion (EFWI) is a powerful tool that can accurately estimate subsurface parameters from multicomponent seismic data, which can provide information useful for characterizing oil and gas reservoirs. We have constructed the relationship between the forward and inverse problems related to the prismatic reflections by considering the multiparameter exact Hessian in realistic elastic media. We numerically analyze the characteristics of the multiparameter exact Hessian and determine that, when prismatic reflections are apparent in multicomponent data, the multiparameter delta Hessian has a strong influence. We develop this in more detail through forward analysis and determine that the multiparameter delta Hessian considers not only the prismatic reflections but also compensates for the primary reflections in multicomponent data. To use the prismatic waves, we develop a migration/demigration approach-based truncated Newton (TN) method in frequency-domain EFWI, whose storage requirements and computational costs are the same as those of the truncated Gauss-Newton (TGN) method. Realistic 2D numerical examples demonstrate that, compared with the TGN method based on the first-order Born approximation, the TN method can converge faster and obtain higher accuracy in the reconstruction of steeply dipping structures.