Developing a tumor model with vessels has been a challenge in microfluidics. This difficulty is because cancer cells can overgrow in a co-culture system. The up-regulation of anti-angiogenic factors during the initial tumor development can hinder neovascularization. The standard method is to develop a quiescent vessel network before loading a tumor construct in an adjacent chamber, which simulates the interaction between a tumor and its surrounding vessels. Here, we present a new method that allows a vessel network and a tumor to develop simultaneously in two linked chambers. The physiological environment of these two chambers is controlled by a microfluidic resistive circuit using two symmetric long microchannels. Applying the resistive circuit, a diffusion-dominated environment with a small 2-D pressure gradient is created across the two chambers with velocity <10.9 nm s-1 and Péclet number <6.3 × 10-5. This 2-D pressure gradient creates a V-shaped velocity clamp to confine the tumor-associated angiogenic factors at pores between the two chambers, and it has two functions. At the early stage, vasculogenesis is stimulated to grow a vessel network in the vessel chamber with minimal influence from the tumor that is still developed in the adjacent chamber. At the post-tumor-development stage, the induced steep concentration gradient at pores mimics vessel-tumor interactions to stimulate angiogenesis to grow vessels toward the tumor. Applying this method, we demonstrate that vasculogenic vessels can grow first, followed by stimulating angiogenesis. Angiogenic vessels can grow into stroma tissue up to 1.3 mm long, and vessels can also grow into or wrap around a 625 μm tumor spheroid or a tumor tissue developed from a cell suspension. In summary, our study suggests that the interactions between a developing vasculature and a growing tumor must be controlled differently throughout the tissue development process, including at the early stage when vessels are still forming and at the later stage when the tumor needs to interact with the vessels.