The materials AVO3 (A = K, Rb, Cs) have been studied at high pressure by energy-dispersive x-ray powder diffraction (EDXRPD) using synchrotron radiation. KVO3 has also been investigated at high pressure by infrared spectroscopy. CsVO3 shows no phase change to 103 kbar. KVO3 exhibits a sluggish phase change from 27 to 48 kbar. A structural model for the high-pressure phase is proposed, in which the vanadate chains slip relative to each other along their axes, generating a monoclinic cell (space group P2/b11, in a non-standard setting). RbVO3 shows a phase change at 40 kbar, indicated by a break in slope for plots of each of the lattice parameters against pressure. No other changes were evident in the EDXRPD pattern at this discontinuity. This is accounted for by a model in which the chains move, relative to each other in the a-direction, maintaining the orthorhombic symmetry of the cell.