Negative Linear Compressibility (NLC), where a material expands in a given direction when subjected to hydrostatic compression, is a rare elastic property that has received much attention recently, but has yet to be used in practical applications. What are the mechanisms responsible for this property in crystals and man-made structures? Are all mechanisms somehow related to the wine-rack model? Can we find an even simpler and more fundamental elucidation of NLC? Following this mechanistic approach, can we then identify “engineering” materials with NLC? To answer these questions, I have used a combination of analytical modelling based on beam theory and finite element analysis, to investigate several structures. At first, I examine in great detail the standard wine-rack in 2D and equivalents in 3D and identify the aspect ratio (close to two) at which NLC is maximum. By adding spacers I demonstrate that a cross is not a necessary condition, and that simpler angle changes in chains are sufficient to generate NLC. Looking for materials with intersecting straight chains, “zig-zag” chains or quasi-helical structures, I find that carbon fibre mats, some extruded polymers and some woods exhibit NLC. Finally, I show that elliptical voids in 2D sheets can also generate NLC in a way related to the wine-rack. This thesis improves the understanding of the mechanism(s) responsible for NLC by proving that a wine-rack is not necessary. Perhaps more importantly it suggests that the property can be exploited in several relatively common materials.