We introduce a method for modeling external tissue support of human arterial hemodynamics. An effective perivascular pressure is considered and the external tissue support model is bas ed on the separati on of total stiffness into arterial wall stiffness and external tissue stiffness. To perform this separation, first the cross-sectional area values at the hypothetical zero pressure state are computed. Finally, a model with two parallel springs is used to determine the material properties of each component. The parameter values are estimated from in vivo data acquired at end diastole. By employing a reduced-order multiscale blood flow model the method is used to study the global effects of external tissue support on the human arterial circulation. The main conclusions are: pressure pulse increases (especially in the proximal aorta), wave speed increases, backward travelling pressure and flow rate waves arrive earlier, the total arterial compliance decreases, cross-sectional area values decrease and oscillations of flow rate and pressure profiles at distal locations are dampened. The computed hemodynamic quantities of interest can be combined with a growth model to predict patient-specific arterial wall remodeling.