Transmission conditions at a bifurcation point in a one-dimensional model of blood vessels are derived by using a three-dimensional model. Both classical Kirchhoff conditions ensuring the continuity of pressure and the vanishing of the flux should be modified in order to reflect properly the elastic properties of blood vessels. A simple approximate method of calculation of new physical parameters in the transmission conditions is proposed. Simplified models of straight sections of arteries with localized defects such as micro-aneurysms and cholesterol plaques are developed; these models also require the statement of some transmission conditions.