Limb compression garments are used to treat a variety of conditions, most notably swelling and oedema, in which a higher than normal amount of fluid accumulates in the interstitium beneath the skin of a patient. According to the present invention, there is provided a limb compression garment 9 for applying a compressive force to a limb of a person when wrapped around that limb, the limb compression garment comprising a planar textile material 11 in which a first plurality of substantially elastic fibres 1 allows the garment to stretch in a first direction in a substantially elastic manner; however, a first plurality of substantially inelastic fibres 5,7 abruptly prevents elastic stretch beyond a maximum extension.