The objective of this paper is to study the mechanical effects caused by the local stiffening of an artery (due to the vascular prosthesis, for instance). At the junction of the host artery and the more rigid implantant, the abrupt change in compliance creates an abnormal stress concentration that initiates an adaptive response in the vascular tissue. The roles of both fluid and solid mechanical phenomena must be considered in the prosthesis design optimization. In this context, even the simple models could provide helpful tools for designing process. We present here a model of blood flow in compliant vessel. The artery is supposed to be an orthotropical thin elastic shell. We obtain the solution by matched asymptotic expansions. The results prove the high flexure concentration close to the compliance jump. It is shown that the use of orthotropical graft may reduce the peak value of these shear forces to a remarkable extent. Waves reflected from the suture and pressure increase in the prosthesis are discussed. Compliance mismatch is shown to reduce the peak value of maximal wall shear stress.