A sensitivity analysis study has been performed on a seven-parameter model of the systemic vascular bed in order to obtain structure reductions appropriate for simulation and estimation. This analysis considers separately the systolic and diastolic transfer functions between arterial and venous pressures in order to divide a non-linear problem in two distinct linear problems. The results obtained refer to nominal parameter values corresponding to normal circulatory conditions in man and supply guide-lines for an application-oriented selection of reduced models. Simple resistance-compliance models are preferred because the inertial effects appear to have only slight influence. In particular, the choice of a five-parameter model seems to be convenient for simulation purposes. An additional structure reduction is suggested to reach reliable results in parameter estimation problems. The resulting model is characterized by three elements: peripheral resistance, arterial compliance and venous compliance.