Published research on drill-core interpretation has been confined to the simple case of multiple drill holes penetrating a planar sequence of layers. This paper investigates the more general situation applicable to deformed terrains, in which the rocks are folded. The analysis is applicable to single, nonlinear drill holes. Fold cylindricity is assumed in some parts of the analysis.Methods are developed in which the relationship of bedding to cleavage and other small-scale structures in drill core is used to determine the orientation of the fold axis, the angle between bedding and cleavage, the vergence with respect to major fold hinges, and the stratigraphic facing of the sequence. The assumptions in each case are clearly spelled out and discussed.These structural parameters may be expressed quantitatively in terms of easily measured drill-core parameters, viz., the angle of inclination of the drill hole, the core angles of bedding, cleavage and lineation, and the direction of younging of any sedimentary structures present in the drill core. This quantified approach permits the introduction of computer programming as an important aid to structural interpretation of drill core.