Abstract Two types of confined etched fission tracks are commonly observed in apatite, TINCLEs (tracks-in-cleavage) and TINTs (tracks-in-track). The TINCLE fission tracks are imaged by the chemical etchant via a crack that intersects the etched surface. TINT fission tracks are etched via intersecting fission tracks that cross the etched surface. We present a simple mathematical model that predicts the TINT fission track density (tracks per unit area) in terms of the confined and surface etchable fission track length distributions and the surface fission track density. For an apatite surface with 4π track registration geometry containing only natural (or induced) fission tracks, the TINT fission track density is predicted to be approximately proportional to (a) the arithmetic mean confined etchable fission track length, and (b) the square of the fission track density on the etched surface. Furthermore, the model predicts that the TINT fission track density can be significantly enhanced by adding charged-particle tracks from an external source to the apatite surface prior to chemical etching. To verify this latter prediction, eight polished crystals of Durango apatite, containing only natural fission tracks from the spontaneous fission of 238U, were placed in close proximity (1–2 mm distant) to a planar 252Cf fission fragment source for times ranging from 0 to approximately 226 h. The TINT fission track density is observed to increase approximately linearly with increasing 252Cf fission track density, a result predicted by the model.