This paper serves as a progress report on our research, specifically focusing on utilizing interval analysis, an existing static analysis method, for detecting vulnerabilities in smart contracts. We present a selection of motivating examples featuring vulnerable smart contracts and share the results from our experiments conducted with various existing detection tools. Our findings reveal that these tools were unable to detect the vulnerabilities in our examples. To enhance detection capabilities, we implement interval analysis on top of Slither [3], an existing detection tool, and demonstrate its effectiveness in identifying certain vulnerabilities that other tools fail to detect.