Burst detection is the activity of finding abnormal aggregates in data streams. Such aggregates are based on sliding windows over data streams. In some applications, we want to monitor many sliding window sizes simultaneously and to report those windows with aggregates significantly different from other periods. We will present a general data structure for detecting interesting aggregates over such elastic windows in near linear time. We present applications of the algorithm for detecting Gamma Ray Bursts in large-scale astrophysical data. Detection of periods with high volumes of trading activities and high stock price volatility is also demonstrated using real time Trade and Quote (TAQ) data from the New York Stock Exchange (NYSE). Our algorithm beats the direct computation approach by several orders of magnitude. Categories and Subject Descriptors H.2.8 [Database Management]: Database Applications-Data Mining Keywords data stream, elastic burst