The existence of bias in samples taken by cross-stream sample cutters has been investigated using three-dimensional discrete element method (DEM) modelling. Detailed quantitative information on overall extraction ratios, size specific extraction ratios, missed and extra sample components can be made by comparing a reference sample to the actual sample. A key advantage of using this modelling approach over physical experimentation is that the reference sample can be measured on precisely the same portion of the stream of material as the actual sample, thereby allowing the elimination of a significant fraction of the variability and allowing statistically significant results to be obtained using many fewer replicates. Quantitative analysis of results broadly supports the commonly-used rule that the cutter aperture should be at least three times the nominal top-size of the material being sampled, but does not support the commonly-used rule requiring increase in cutter aperture if the cutter speed exceeds 0.6 m/s. Sampler performance can be understood in terms of the balance of forces in the congested region of material formed by the slowing of the particle stream due to collisional interactions around the mouth of the cutter.