This paper reports the effect of elevated pressure on the invasive phenotype of patterned three-dimensional (3D) aggregates of MDA-MB-231 human breast cancer cells. We found that the directionality of the interstitial pressure profile altered the frequency of invasion by cells located at the surface of an aggregate. In particular, application of pressure at one end of an aggregate suppressed invasion at the opposite end. Experimental alteration of the configuration of cell aggregates and computational modeling of the resulting flow and solute concentration profiles revealed that elevated pressure inhibited invasion by altering the chemical composition of the interstitial fluid near the surface of the aggregate. Our data reveal a link between hydrostatic pressure, interstitial convection, and invasion.