Submerged plants in shallow lakes are subject to pulling forces arising from waves, currents and grazing birds. Such forces can cause anchorage failure (mainly dislodgement of the root system) or breaking failure of the stems. Both lead to loss of fitness but uprooting is more damaging because many perennial species can replace broken shoot systems. We investigated 12 abundant species (Ceratophyllum demersum, Chara sp., Eleogiton fluitans, Elodea canadensis, Myriophyllum spicatum, Najas marina, Potamogeton natans, P. obtusifolius, P. pectinatus, P. pusillus, Utricularia vulgaris and Zannichellia palustris) in 28 shallow lakes in the UK and the Netherlands. We measured the anchorage and breaking strengths of individual plants of different sizes. Anchorage strength depends on the cohesive strength of the sediment and the size of the root system. The undrained shear-strength of sediments in shallow lakes varied more than 50-fold, but all were substantially weaker than terrestrial soils. Anchorage strength was modelled using the product of sediment cohesive strength and four measures of root-system size. A transformation of plan-form area (raising it to the power 2/3) that represented the hemispherical surface area of the root ball was consistently the best predictor of anchorage strength. Breaking strength was a linear function of stem cross-sectional area in all species. Breaking stresses were comparable with those of marine algae and non-lignified terrestrial plants. The results were used, in combination with plant allometric relationships, to predict the fates of four of the species when challenged with the largest waves likely to be encountered in a 10-year period, and the even greater forces exerted by grazing birds. We show that sediment strength and plant size determine whether plants break or uproot. A careful balance between investment in anchorage and in breakage resistance is needed to survive in the fluctuating physical environment of lakes. Pulling forces experienced by aquatic plants are distinct from the mainly bending forces on more rigid land plants. We provide the first theoretical and quantitative framework for understanding their effects. Anchorage failure associated with the soft sediments of eutrophic lakes is likely to be a factor in the loss of macrophyte communities and an important factor in their restoration.