In this paper, a mathematical model of the mechanical behaviour of prosthetic blood vascular structures is analysed when taking into account effects of finite deformations, residual stresses which can be induced by fabrication processes and the composite nature of the material constituting those structures. The case of particular applied strains, viewed as arising during surgical manipulation and implying axial and circular shear stresses, is also studied. The resulting distribution of stresses within the wall shows large gradients which can be reduced when the effects of adequate pre-existing initial stresses are present.