Microstructural features of eurypterid cuticles are analysed from a biomechanical viewpoint: some fibrous elements are now considered to resemble the macrofibres of extant arthropod cuticles; possible preferred orientation zones in Mycterops are related to directional stresses; pore canals are not viewed as acting as crack-stoppers but laminae (sensu Dennell 1978) may have served this function. Could some eurypterids have walked on land?—this problem is approached by using extant Limulus as a model. It leads on to the use of scaling exponents to determine the limits that possessing an exoskeleton places on the size of land arthropods: moulting may be the limiting factor. Possible critical factors limiting the size of aquatic arthropods are discussed briefly.