Stochastic simulations are often sensitive to the randomness source that characterizes the statistical quality of their results. Consequently, we need highly reliable Random Number Generators (RNGs) to feed such applications. Recent developments try to shrink the computation time by using more and more General Purpose Graphics Processing Units (GP-GPUs) to speed-up stochastic simulations. Such devices bring new parallelization possibilities, but they also introduce new programming difficulties. Since RNGs are at the base of any stochastic simulation, they also need to be ported to GP-GPU. There is still a lack of well-designed implementations of quality-proven RNGs on GP-GPU platforms. In this paper, we introduce ShoveRand, a framework defining common rules to generate random numbers uniformly on GP-GPU. Our framework is designed to cope with any GPU-enabled development platform and to expose a straightforward interface to users. We also provide an existing RNG implementation with this framework to demonstrate its efficiency in both development and ease of use.