In the mobile edge computing environment, caching data in edge storage systems can significantly reduce data retrieval latency for users while saving the costs incurred by cloud-edge data transmissions for app vendors. Existingedge data caching(EDC) methods prioritize popular data and aim to minimize users’ data retrieval latency and system storage costs jointly. However, these EDC methods often rely on the assumption that data popularity always follows certain distributions. As a result, they cannot properly adapt to the fluctuations in data popularity due to user mobility or unexpected increases in user demands. Meanwhile, unlike cloud data centers, complex and fragile edge servers are more likely to experience physical failures or network outages, presenting new challenges for EDC strategies. Specifically, when an edge server fails or experiences an outage, cached data may become temporarily unavailable, leading to increased latency as requests are redirected to alternative servers or the cloud. In this paper, to enableuncertainty-aware edge data caching(uEDC), we first model the problem as a robust optimization problem and propose an optimal algorithm named uEDC-B to find the optimal uEDC solution. To address the high computational complexity of uEDC-B, we introduce an approximate algorithm named uEDC-L based on linear decision rules. Theoretical analysis and extensive experiments on a real-world dataset demonstrate that the proposed methods outperform two state-of-the-art approaches in handling the uncertainties in data popularity and edge server failure with a significant performance improvement of 59.27% in data retrieval latency and 55.07% in data caching cost.