Universal machine learning interatomic potentials have emerged as efficient tools for materials simulation, yet their reliability for elastic property prediction remains unclear. Here, we present a systematic benchmark of four uMLIPs -- MatterSim, MACE, SevenNet, and CHGNet -- against first-principles data for nearly 11\,000 elastically stable materials from the Materials Project database. The results show that SevenNet achieves the highest accuracy, MACE and MatterSim balance accuracy with efficiency, while CHGNet performs less effectively overall. To further improve predictive quality, we perform targeted fine-tuning on all four uMLIPs using strained configurations derived from 185 high-error materials. After fine-tuning, CHGNet shows the most substantial improvement in overall accuracy, with MatterSim and SevenNet also benefiting from the fine-tuning, whereas MACE shows limited robustness to this procedure. This work provides quantitative guidance for model selection and data refinement, advancing uMLIPs toward reliable applications in mechanical property prediction.