Bedding-parallel fibrous veins are common worldwide in sedimentary basins, especially within strata of low permeability. The term "beef" refers to bedding-parallel veins of fibrous minerals, where the fibres are mutually parallel and have formed quasi-vertically. More complex on a smaller scale are "conein- cone" structures, yet these are also common within bedding-parallel veins. For both beef and conein- cone we have compiled a worldwide catalogue (157 localities). Typically, the veins consist mainly of white gangue minerals (for example, calcite, gypsum, or quartz), but may also contain accessory minerals of economic interest (for example, bitumen, sulphides, emerald, pitchblende or gold). Fluid inclusions may contain oil or gas. Calcite beef (110 localities) is common in organic-rich shale of marine-carbonate origin, especially of (1) CambrianeOrdovician, (2) DevonianeCarboniferous, (3) early Jurassic, or (4) Cretaceous to Palaeogene ages. Gypsum beef (30 localities) is common in evaporitic or lacustrine strata of continental origin, especially of Triassic or Neogene ages. Quartz beef (17 localities) is common within meta-turbidite sequences, especially of Ordovician or Proterozoic ages. Because these modal ages seem to reflect climatic controls, we infer that the fibre-forming mineral species have not travelled far, vertically. The same conclusion holds for accessory minerals. Typical temperatures of formation are (1) up to 60 C for gypsum beef, (2) 70 C to 120 C for calcite beef, and (3) 200 C to 350 C for quartz beef. Hydrocarbon-bearing calcite beef may be a good indicator of a petroleum system, in which oil or gas migrate, together with aqueous solutions. We argue that beef and cone-in-cone layers result from tensile fracturing and vertical dilation, coeval with fibre growth. Possible causes are either (1) force of crystallization, or (2) seepage forces, due to fluid overpressure. For layers that form at depths of several km, fluid overpressure is the more likely cause.