In pre-stack seismic inversion, accurate prediction of elastic parameters, such as P- and S-wave velocities, is crucial for reservoir characterization, including fluid identification and lithology discrimination. In recent years, deep learning-based reservoir parameter prediction has been widely applied. However, deep neural networks are usually regarded as black boxes with limited physical interpretability, and it remains challenging to characterize the mapping relationship between seismic data and rock elasticity. In addition, the lack of S-wave velocity (Vs) samples in field well-logging data limits the training accuracy and reliability of deep learning models. To address these problems, we propose a multi-frequency-band parallel Transformer U-Net (TransUNet) inversion framework with SHapley Additive exPlanations (SHAP) analysis. First, SHAP analysis is introduced to clarify the effects of seismic data across different frequency bands on rock elastic parameters, indicating the necessity of frequency decomposition for multi-parameter prediction. Then, a multi-frequency-band parallel TransUNet architecture is developed, in which simultaneous multi-trace input is used to account for lateral continuity in inversion, and the global receptive field of the Transformer is incorporated to further improve inversion resolution and accuracy. Finally, to handle the shortage of S-wave velocity samples, a stepwise transfer learning strategy is adopted. A large number of P-wave velocity and density samples are first used to optimize the parameters of the backbone network. Subsequently, with the backbone network frozen, a small number of S-wave velocity samples are used to fine-tune the output module, thereby enabling effective seismic S-wave velocity inversion. This study investigates the mapping relationship between frequency-decomposed seismic data and multiple reservoir elastic parameters and provides a deep learning-based inversion strategy for reservoir elastic parameters under limited S-wave velocity data. The proposed method can contribute to the detailed characterization of complex reservoirs.