A reactor for supercritical water oxidation comprises an essentially vertical reactor section (11) and an essentially non-vertical reactor section (12), wherein the vertical reactor section has a cross-sectional area which is substantially larger than the cross-sectional area of the non-vertical reactor section. The vertical reactor section has an inlet (14) in an upper portion thereof for receiving (17) a flow containing organic material and water, and an outlet (16) in a lower portion thereof for outputting (20) the flow. Both the vertical and the non-vertical reactor sections are configured to oxidize organic material in the flow through supercritical water oxidation.