The paper suggests an approach to network attack modeling and security evaluation which is realized in advanced Security Information and Event Management (SIEM) systems. It is based on modeling of computer network and malefactors' behaviors, building attack graphs, processing current alerts for real-time adjusting of particular attack graphs, calculating different security metrics and providing security assessment procedures. The novelty of the proposed approach is the use of special algorithms for construction, modification and analysis of attack graphs aimed at rapid security evaluation. This allows using this approach in SIEM systems that operate in near-real time. The generalized architecture of the Attack Modeling and Security Evaluation Component (AMSEC), as one of the main analytical components of SIEM systems, is outlined. The main components and techniques for attack modeling and security evaluation are defined. A prototype of the AMSEC is presented. Experiments with this prototype are evaluated.