Detachment folds form above, below, or above and below bed-parallel thrusts where thrust displacement is transferred into folding. Geometric and kinematic models are developed for individual single-layer detachment folds formed above the tip line of a thrust. We analyze three different detachment fold shapes (kink bands, chevron, and box detachment folds) and consider three principal detachment fold models: (1) constant limb dip where the detachment fold grows by limb lengthening, (2) constant limb length where the detachment fold grows by limb rotation, and (3) variable limb length and variable limb dip where the detachment fold grows by both limb rotation and limb lengthening. The allowance for variable forelimb thickness and excess layer-parallel shear enables us to develop a wide range of possible detachment fold geometry. The geometric validity fields for folds with excess parallel shear are reduced when forelimb thinning takes place. Folds formed with constant limb length are likely to lock up in the initial amplification stages, whereas larger amounts of shortening can be taken up by folds formed with variable limb length. The manner in which a fold evolves affects the fracture and porosity features of the folded strata. Therefore, determining which mechanism operated to form a specific detachment fold is of particular importance in hydrocarbon exploration. The models we present are aimed at permitting more accurate geometric and kinematic interpretations of individual detachment folds. Examples of detachment folds are analyzed to illustrate the potential benefits and limitations of the geometric model presented.