A device for cutting expanded polystyrene foam volumes obtaining double-curvature surfaces, comprising a first pair of linear guides, wherein a block of material in its movement faces a rectangular frame which is arranged perpendicularly to the movement path of the block of material passing through this rectangular frame during cutting, said rectangular frame having a fixed position and being supported on a horizontal frame having four support legs, whereby the cutting device remains sustained on the floor; wherein the rectangular frame has a flexible blade; characterized in that over each of the linear guides two pairs of plates arranged over skids are movable, wherein each pair of plates is connected by a horizontal beam; the two pairs of plates and the pair of horizontal beams allow supporting and fixing a block of material of expanded polystyrene foam for cutting; the block of material supported on the plates is displaceable by a first pair of synchronous belts and pulleys, which are driven by a first pair of step motors, which are simultaneously activated, wherein the flexible blade can be of steel or similar material which is covered with a sheath of thermal and electrical insulation, over which a resistive heating wire is helically wound, through which an electrical current can be circulated for heating the resistive heating wire, wherein the heat vaporizes a zone of the material of the block just before making physical contact with it during the displacement thereof, wherein the flexible blade is sustained at its ends by gearwheels (20, 30), and wherein the rectangular frame is formed by four sides, and in its upper and lower sides (115, 116), each one of them supports a vertical rail (120, 125), wherein each vertical support rail (120, 125) has a step motor in its lower side that can be simultaneously or alternately activated; wherein each one of them moves a pinion (21, 31) to drive the gearwheel (20, 30), wherein the pinion (21, 31) that drives the gearwheel (20, 30), transmits the movement to the ends of the flexible blade; each vertical support rail (120, 125) slidable through skids fixed to a plate (121, 126) respectively, so as to obtain a vertical motion for each of the vertical support rails (120, 125); each one of the plates (121, 126) is supported on a horizontal sliding plate (122, 127) respectively, so that they can move on the respective rail corresponding to the upper and lower sides (115, 116) of the rectangular frame respectively, which allows each vertical support rail (120, 125) to horizontally move within a limit lower than the length of the side (115, 116); the vertical movements are transmitted through spindles rotated by step motors, which can be simultaneously or alternately activated; and the horizontal movements are transmitted through synchronous pulleys and belts, which are rotated by step motors, which can be simultaneously or alternately activated. characterized in that over each of the linear guides two pairs of plates arranged over skids are movable, wherein each pair of plates is connected by a horizontal beam; the two pairs of plates and the pair of horizontal beams allow supporting and fixing a block of material of expanded polystyrene foam for cutting; the block of material supported on the plates is displaceable by a first pair of synchronous belts and pulleys, which are driven by a first pair of step motors, which are simultaneously activated, wherein the flexible blade can be of steel or similar material which is covered with a sheath of thermal and electrical insulation, over which a resistive heating wire is helically wound, through which an electrical current can be circulated for heating the resistive heating wire, wherein the heat vaporizes a zone of the material of the block just before making physical contact with it during the displacement thereof, wherein the flexible blade is sustained at its ends by gearwheels (20, 30), and wherein the rectangular frame is formed by four sides, and in its upper and lower sides (115, 116), each one of them supports a vertical rail (120, 125), wherein each vertical support rail (120, 125) has a step motor in its lower side that can be simultaneously or alternately activated; wherein each one of them moves a pinion (21, 31) to drive the gearwheel (20, 30), wherein the pinion (21, 31) that drives the gearwheel (20, 30), transmits the movement to the ends of the flexible blade; each vertical support rail (120, 125) slidable through skids fixed to a plate (121, 126) respectively, so as to obtain a vertical motion for each of the vertical support rails (120, 125); each one of the plates (121, 126) is supported on a horizontal sliding plate (122, 127) respectively, so that they can move on the respective rail corresponding to the upper and lower sides (115, 116) of the rectangular frame respectively, which allows each vertical support rail (120, 125) to horizontally move within a limit lower than the length of the side (115, 116); the vertical movements are transmitted through spindles rotated by step motors, which can be simultaneously or alternately activated; and the horizontal movements are transmitted through synchronous pulleys and belts, which are rotated by step motors, which can be simultaneously or alternately activated.