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tokens: time varies with rigidity E / Z , with Z the charge number, as t res ∝ ( E / Z ) s with s ≃ 0.4–0.6. There are a number of codes that model Galactic CR propagation and the CR interactions (losses, spallation, decay of unstable nuclei, and re-acceleration) in the Galaxy, such as galprop , see Strong et al. ( 2010 ), dragon , see Evoli et al. ( 2008 ), and crpropa , see Alves Batista et al. ( 2016 ). In this paper, we do not take into account the effects of CR advection by the Galactic winds, energy losses, and re-acceleration. We also do not consider the network of nuclear reactions that leads to the production of secondary CRs. These effects will be considered in future work. However, in these codes one usually limits the calculations to models with cylindrical symmetry models with an effective diffusion coefficient D , thereby neglecting the influence of the geometry and strength of the GMF on CR diffusion. Recently, some efforts has been taken to consider anisotropic diffusion models for Galactic CRs, see Evoli et al. ( 2017 ). We will consider anisotropic diffusion of CRs inside the Galaxy. We note that a similar calculation, again employing stochastic differential equations, has been applied to the interplanetary transport and acceleration of solar energetic particles in the solar wind see Dröge et al. ( 2010 ) and the references therein. The outline of this paper is as follows: in Section 2 , we discuss the GMF and introduce the main features of the Jansson–Farrar. In Section 3 , we present our numerical solution method to the CR diffusion, based on the Itô formulation of stochastic differential equations, using relevant input, like the diffusion tensor and its connection to the GMF in Section 3.1 . The grammage calculation is discussed in Section 3.3 . In Section 4 , we present the spatial distribution of the CRs from a single source the associated residence time distribution, as well as the grammage of CR particles. We do this for various combinations of parallel and perpendicular diffusion. Section 5 discusses the implications of the results presented in this paper and summarizes our conclusions. 2 MODEL FOR THE GMF The magnetic field in the diffuse interstellar medium (ISM) has two distinct components: a large-scale () regular field, as well as a small-scale turbulent component. The strength of the total magnetic field in the Galaxy has been estimated of about 6±2 μG, see Beck ( 2001 ) and Haverkorn ( 2015 ), with the amplitude of the random field comparable to that of the large-scale field. The large-scale GMF affects the propagation of CRs (Strong et al. 2007 ), the dynamics of molecular clouds and star formation, see Hennebelle Falgarone ( 2012 ). In this paper, we use the GMF model of Jansson Farrar ( 2012a ) and Jansson Farrar ( 2012b ) for this large-scale (regular) field. This model matches the WMAP 7 22 GHz synchrotron intensity map and the Galactic Faraday rotation data obtained from polarization measurements of background