Understanding how users' search behavior is influenced by real world events is important both for social science research and for designing better search engines for users. In this paper, we study how to model the influence of events on user queries by framing it as a novel data mining problem. Specifically, given a text description of an event, we mine the search log data to identify queries that are triggered by it and further characterize the temporal trend of influence created by the same event on user queries. We solve this data mining problem by proposing computational measures that quantify the influence of an event on a query to identify triggered queries and then, proposing a novel extension of Hawkes process to model the evolutionary trend of the influence of an event on search queries. Evaluation results using news articles and search log data show that the proposed approach is effective for identification of queries triggered by events reported in news articles and characterization of the influence trend over time, opening up many interesting opportunities of applications such as comparative analysis of influential events and prediction of event-triggered queries by users.