This letter investigates the uplift capacity of plate anchors in granular soils. Simulations based on a discrete-element method are used to measure the uplift capacity of anchors of differing widths to embedment B/H and width to grain-size B/d ratios. Results confirm that the uplift capacity of anchors with a large B/d ratio is well described by existing models developed from continuum mechanics, with no grain-size effect. In contrast, results reveal a strong deviation from these models for anchors with relatively small B/d ratios. A semi-empirical model is introduced that captures this strong grain-size effect. This model is further supported by a micro-mechanical analysis, indicating that anchor uplift capacities are not only governed by a frustum mechanism predicted by continuum mechanics but also involve the mobilisation of grains surrounding this frustum. These results and model are particularly important to rationalise uplift capacities measured in small-scale experiments, typically involving small B/d ratios, and to safely upscale them to larger anchor size relevant to field applications.