Implementation of adequate measures to assess and monitor droughts is recognized as a major matter challenging researchers involved in water resources management. The objective of this study is to assess the hydrologic drought characteristics from the historical rainfall records of Kuwait with arid environment by employing the criterion of Standardized Precipitation Index (SPI). A wide range of monthly total precipitation data from January 1967 to December 2009 is used for the assessment. The computation of the SPI series is performed for intermediate- and long-time scales of 3, 6, 12, and 24 months. The drought severity and duration are also estimated. The bivariate probability distribution for these two drought characteristics is constructed by using Clayton copula. It has been shown that the drought SPI series for the time scales examined have no systematic trend component but a seasonal pattern related to rainfall data. The results are used to perform univariate and bivariate frequency analyses for the drought events. The study will help evaluating the risk of future droughts in the region, assessing their consequences on economy, environment, and society, and adopting measures for mitigating the effect of droughts.