Due to the limitations of two-dimensional models in mimicking intratumoral drug delivery, three-dimensional tumor spheroid-on-chip models have been considered recently. Even though various models have been proposed in this field, many unknowns still exist about their reliability in imitating in vivo conditions. In addition, most of these models neglect the replication of drug transport from the bloodstream. In the current research, considering the interface of tumor and blood vessels, new designs of microfluidic devices are developed to resemble the in vivo conditions more closely. Then, drug transport in the proposed models is studied numerically using porous media theory under dynamic conditions. The simulation results of drug concentration, cell viability, fluid shear stress, and pressure distributions are compared with those of a solid tumor. As the results demonstrate, our proposed models can well mimic the in vivo conditions, including drug delivery through blood vessels. Therefore, in addition to developing tumor spheroid-on-chip models resembling tumor-vessel interaction, the present study provides a strong strategy to evaluate the reliability of in vitro models in replicating intratumoral drug delivery.