Alterations of blood flow patterns strongly correlate with arterial wall diseases such as atherosclerosis and aneurysm. Here, a simple, pumpless, close‐loop, easy‐to‐replicate, and miniaturized flow device is introduced to concurrently expose 3D engineered vascular smooth muscle tissues to high‐velocity pulsatile flow versus low‐velocity disturbed flow conditions. Two flow regimes are distinguished, one that promotes elastin and impairs collagen I assembly, while the other impairs elastin and promotes collagen assembly. This latter extracellular matrix (ECM) composition shares characteristics with aneurysmal or atherosclerotic tissue phenotypes, thus recapitulating crucial hallmarks of flow‐induced tissue morphogenesis in vessel walls. It is shown that the mRNA levels of ECM of collagens and elastin are not affected by the differential flow conditions. Instead, the differential gene expression of matrix metalloproteinase (MMP) and their inhibitors (TIMPs) is flow‐dependent, and thus drives the alterations in ECM composition. In further support, treatment with doxycycline, an MMP inhibitor and a clinically used drug to treat vascular diseases, halts the effect of low‐velocity flow on the ECM remodeling. This illustrates how the platform can be exploited for drug efficacy studies by providing crucial mechanistic insights into how different therapeutic interventions may affect tissue growth and ECM assembly.