For each kind of distributed computing infrastructures, i.e., clusters, grids, clouds, data centers, or supercomputers, storage is a essential component to cope with the tremendous increase in scientific data production and the ever-growing need for data analysis and preservation. Understanding the performance of a storage subsystem or dimensioning it properly is an important concern for which simulation can help by allowing for fast, fully repeatable, and configurable experiments for arbitrary hypothetical scenarios. However, most simulation frameworks tailored for the study of distributed systems offer no or little abstractions or models of storage resources. In this paper, we detail the extension of SimGrid, a versatile toolkit for the simulation of large-scale distributed computing systems, with storage simulation capacities. We first define the required abstractions and propose a new API to handle storage components and their contents in SimGrid-based simulators. Then we characterize the performance of the fundamental storage component that are disks and derive models of these resources. Finally we list several concrete use cases of storage simulations in clusters, grids, clouds, and data centers for which the proposed extension would be beneficial.