Cognitive Radio (CR) is a promising solution to solve the problem of limited spectrum and poor bandwidth utilization in wireless networks by opportunistieally exploiting the available wireless spectrum. Despite the numerous advantages of CR technology, it imposes unique challenges for modeling and simulation due to dynamic spectrum sensing and the high fluctuations in the spectrum utilization as well as diverse set of components that form a CR network. Therefore, to develop a model for CR network and execute the distributed simulation, it is critical to have a complete understanding of (1) an analytical model that incorporates all components of a CR network and (2) a framework that layout all necessary tools and services needed for a successful modeling and simulation. In this paper, we have two research contributions. First, we present an analytical model of CR by identifying components necessary for a design of a typical CR and classify them in the context of modeling and simulation. A design of a CR network includes the software defined radio (SDR), spectrum sensing, and communication channels. The layers of the analytical model encapsulate the SDR, spectrum sensing techniques, and the communication channels. Second, we construct a theoretical representation of a CR by specifying its unique characteristics needed for modeling and simulation. We show the mapping of these characteristics into a layered architecture framework which ease the model formulization and simplify the simulation of a complex CR network.