Several distinct fluid flow phenomena occur in solid tumors, including intravascular blood flow and interstitial convection. Interstitial fluid pressure is often raised in solid tumors, which can limit drug delivery. To probe low-velocity flow in tumors resulting from raised interstitial fluid pressure, we developed a novel magnetic resonance imaging (MRI) technique named convection-MRI, which uses a phase-contrast acquisition with a dual-inversion vascular nulling preparation to separate intra- and extra-vascular flow. Here we report the results of experiments in flow phantoms, numerical simulations, and tumor xenograft models to investigate the technical feasibility of convection-MRI. We observed a significant correlation between estimates of effective fluid pressure from convection-MRI with gold-standard, invasive measurements of interstitial fluid pressure in mouse models of human colorectal carcinoma. Our results show how convection-MRI can provide insights into the growth and responsiveness to vascular-targeting therapy in colorectal cancers.