Several lumped parameter, or zero-dimensional (0-D), models of the microcirculation are coupled in the time domain to the nonlinear, one-dimensional (1-D) equations of blood ﬂow in large arteries. A linear analysis of the coupled system, together with in vivo observations, shows that: (i) an inﬂow resistance that matches the characteristicimpedanceof the terminal arteriesis requiredtoavoidnon-physiological wave reﬂections; (ii) periodic mean pressures and ﬂow distributions in large arteries depend on arterial and peripheral resistances, but not on the compliances and inertias of the system, which only affect instantaneous pressure and ﬂow waveforms; (iii) peripheral inertias have a minor effect on pulse waveforms under normal conditions; and (iv) the time constant of the diastolic pressure decay is the same in any 1-D model artery, if viscous dissipation can be neglected in these arteries, and it depends on all the peripheral compliances and resistances of the system. Following this analysis, we propose an algorithm to accurately estimate peripheral resistances and compliances from in vivo data. This algorithm is veriﬁed against numerical data simulated using a 1-D model network of the 55 largest human arteries, in which the parameters of the peripheral windkessel outﬂow models are known a priori. Pressure and ﬂow waveforms in the aorta and the ﬁrst generation of bifurcations are reproduced with relative root-mean-square errors smaller than 3%.