Recently, several Fault Attacks (FAs) which target modern Central Processing Units (CPUs) have emerged. These attacks are studied from a practical point of view and, due to the modern CPUs complexity, the underlying fault effect is usually unknown. In this article, we focus on the characterization of a perturbation (the fault model) on modern CPU. For that, we introduce the first approach to characterize the fault model on modern CPU from the Instruction Set Architecture (ISA) level to the micro-architectural level. This fault model helps at determining which micro-architecture elements are disrupted and how. Our fault model aims at finding original attack paths and design efficient countermeasures. To confront our approach to real modern CPUs, we apply our approach on ARM and x86 architectures CPUs, mainly on the BCM2837 and an Intel Core i3.