A new model predicts the searching speed of terrestrial predators feeding on sedentary prey, when maximizing net energy intake. The model predicts there is a critical prey density above which an animal should always maximize searching speed and below which it should stop foraging. It is predicted the critical density should increase with increases in the incremental cost of locomotion, and decrease as the energy content of the prey increases. When the energy cost of handling prey, relative to the resting cost, is greater than the fixed costs of locomotion, increases in handling time should lead to increases in the critical density. Conversely when the cost of handling prey is lower than the fixed cost of locomotion, increases in handling time lead to decreases in the critical density.