In recent years, attack trees have been developed to describe processes by which malicious users attempt to exploit or break computer software and/or networks. Attack trees are a way of decomposing, visualizing, and determining the cost or likeliness of attacks. Similarly, Petri Nets (PNs) are graphical representations of a system or process used for modeling, formal analysis, and design verification. PNs are easy to build and simulate using a myriad of available tools. There are a number of subclasses of PNs, including Colored, Timed, Stochastic, etc. This paper focuses on the use of Generalized Stochastic PNs (GSPNs) to model and analyze Attack Trees with the ultimate goal of automating the analysis using simulation tools.The results of this simulation and analysis can be used to further refine the Attack Tree or to develop countermeasures.