We have developed a microfluidic device that mimics the delivery and systemic clearance of drugs to heterogeneous three-dimensional tumor tissues in vitro. Nutrients delivered by vasculature fail to reach all parts of tumors, giving rise to heterogeneous microenvironments consisting of viable, quiescent and necrotic cell types. Many cancer drugs fail to effectively penetrate and treat all types of cells because of this heterogeneity. Monolayers of cancer cells do not mimic this heterogeneity, making it difficult to test cancer drugs with a suitable in vitro model. Our microfluidic devices were fabricated out of PDMS using soft lithography. Multicellular tumor spheroids, formed by the hanging drop method, were inserted and constrained into rectangular chambers on the device and maintained with continuous medium perfusion on one side. The rectangular shape of chambers on the device created linear gradients within tissue. Fluorescent stains were used to quantify the variability in apoptosis within tissue. Tumors on the device were treated with the fluorescent chemotherapeutic drug doxorubicin, time-lapse microscopy was used to monitor its diffusion into tissue, and the effective diffusion coefficient was estimated. The hanging drop method allowed quick formation of uniform spheroids from several cancer cell lines. The device enabled growth of spheroids for up to 3 days. Cells in proximity of flowing medium were minimally apoptotic and those far from the channel were more apoptotic, thereby accurately mimicking regions in tumors adjacent to blood vessels. The estimated value of the doxorubicin diffusion coefficient agreed with a previously reported value in human breast cancer. Because the penetration and retention of drugs in solid tumors affects their efficacy, we believe that this device is an important tool in understanding the behavior of drugs, and developing new cancer therapeutics.