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Peatland restoration using cell bunding relies on low peat embankments to retain target water levels, yet seepage through such peat bunds is difficult to predict because hydraulic conductivity varies over orders of magnitude and is strongly spatially structured. This study quantifies steady-state seepage uncertainty for a representative two-layer bund system at All Saints Bog (Ireland) using a random finite element framework. Layer-specific conductivity statistics were obtained from laboratory tests on undisturbed peat cores and represented as lognormal in physical space. Spatial heterogeneity was modelled using anisotropic Gaussian random fields generated by the spectral representation method within a 3 × 3 factorial design, spanning three variance levels and three correlation-scale settings for both bund and base layers. For each group, ten independent realisations were mapped element-wise in a PLAXIS 2D seepage model and solved under realistic operational heads from 0.00 to 0.35 m. Discharge was extracted at multiple vertical control sections and at the downstream toe, and analysed using ensemble seepage rate – head (Q–H) relationships, local sensitivity, variance decomposition, and exceedance statistics. Seepage rate increased nonlinearly with head, and uncertainty amplified towards the seepage face toe, where coefficients of variation at H=0.35 m ranged from 8% to 36% across groups (compared with 6% to 21% mid-bund). Upper-tail behaviour strengthened with increasing variance and longer correlation scales; at the toe, Q95 and Q99 at H=0.35 m reached 8.60×10−4 and 1.07×10−3 Ls−1m−1, respectively. The results show that exceedance-based seepage quantiles provide more decision-relevant estimates than mean values alone and offer a practical basis for reliability-informed bund design. These results can also be used to help modelling the overall performance of such peatland bund network used in the restoration of raised bogs.