Material heterogeneities cause local stress concentrations which serve as initial sites for nonlinear behaviours such as plastification or failure. With FFT-based full-field computations, these stress concentrations can be investigated stochastically by simulating sufficiently large ensembles of microstructures. In the case of polycrystalline elasto-plastic metals, it is suspected in the literature that critical stresses in the slip systems converge to Gaussian normal distributions as the sample size of microstructures increases [1]. We investigate stress concentrations in statistically isotropic FCC crystals through a large ensemble study of 200 computer-generated microstructures of 512 grains each. By considering a single grain orientation in different microstructural neighbourhoods, we find that the critical stresses are not normally distributed, but more closely approach a lognormal distribution. Furthermore, the stress concentrations are significantly more pronounced near the grain boundaries, featuring both higher and lower stresses than the grain’s center. As the yield stress of the material is locally exceeded, the stress fluctuations decrease initially. With full plastification, stress fluctuations increase again as hardening causes plastic heterogeneities. The results in the linear elastic regime closely agree with analytical approximations given by the Maximum Entropy Method [2]. [1] Brenner, R., Lebensohn, R. A., & Castelnau, O. (2009). Elastic anisotropy and yield surface estimates of polycrystals. International Journal of Solids and Structures, 46(16), 3018-3026. [2] Kreher, W., & Pompe, W. (1989). Internal stresses in heterogeneous solids (Vol. 9). De Gruyter Akademie Forschung.