It is commonly accepted that arrays of en échelon veins occur either singularly or in conjugate pairs. Bulk finite plane strain is accompanied by these singular or conjugately arranged arrays when their formation and subsequent displacement occur in the same kinematic framework. A new geometric and kinematic model for vein arrays is proposed which takes into account the effects of bulk non-plane-strain deformations on the evolving arrays. In this model, four sets of arrays develop during coaxial non-plane-strain deformations and two non-conjugate sets of arrays develop during non-coaxial non-plane-strain deformations. The formation of singular and conjugate arrays is restricted to bulk plane-strain deformations. This model is the natural extension to the brittle-ductile realm of models proposed for the geometry and kinematics of brittle faults formed during non-plane-strain deformations. En échelon vein arrays mapped in central Australia which cannot be understood as simple conjugate structures, are interpreted as having formed during a bulk non-coaxial non-plane-strain deformation.