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This paper presents a fast approach to simulating muons produced in interactions of the SPS proton beams with the target of the SHiP experiment. The SHiP experiment will be able to search for new long-lived particles produced in a 400 GeV/c SPS proton beam dump and which travel distances between fifty metres and tens of kilometers. The SHiP detector needs to operate under ultra-low background conditions and requires large simulated samples of muon induced background processes. Through the use of Generative Adversarial Networks it is possible to emulate the simulation of the interaction of 400 GeV/c proton beams with the SHiP target, an otherwise computationally intensive process. For the simulation requirements of the SHiP experiment, generative networks are capable of approximating the full simulation of the dense fixed target, offering a speed increase by a factor of O(10^6). To evaluate the performance of such an approach, comparisons of the distributions of reconstructed muon momenta in SHiP's spectrometer between samples using the full simulation and samples produced through generative models are presented. The methods discussed in this paper can be generalised and applied to modelling any non-discrete multi-dimensional distribution.