There is a clinical need for better blood vessel substitutes, as current surgical procedures are limited by the availability of suitable autologous vessels and suboptimal behavior of synthetic grafts in small caliber arterial graft (<5  mm) applications. The aim of the present study was to compare the mechanical properties of arterial and venous tissue-engineered vascular constructs produced by the self-assembly approach using cells extracted from either the artery or vein harvested from the same human umbilical cord. The production of a vascular construct comprised of a media and an adventitia (TEVMA) was achieved by rolling a continuous tissue sheet containing both smooth muscle cells and adventitial fibroblasts grown contiguously in the same tissue culture plate. Histology and immunofluorescence staining were used to evaluate the structure and composition of the extracellular matrix of the vascular constructs. The mechanical strength was assessed by uniaxial tensile testing, whereas viscoelastic behavior was evaluated by stepwise stress-relaxation and by cyclic loading hysteresis analysis. Tensile testing showed that the use of arterial cells resulted in stronger and stiffer constructs when compared with those produced using venous cells. Moreover, cyclic loading demonstrated that constructs produced using arterial cells were able to bear higher loads for the same amount of strain when compared with venous constructs. These results indicate that cells isolated from umbilical cord can be used to produce vascular constructs. Arterial constructs possessed superior mechanical properties when compared with venous constructs produced using cells isolated from the same human donor. This study highlights the fact that smooth muscle cells and fibroblasts originating from different cell sources can potentially lead to distinct tissue properties when used in tissue engineering applications.