In order to reduce the amount of computation required for ray tracing and facilitate simulating of changes in workpiece shape even on an inexpensive, low-performance computer, a device for displaying a cutting simulation includes: a rendered workpiece image update section for updating by ray tracing a portion of a rendered workpiece image buffer and a rendered workpiece depth buffer, the portion being associated with a rendering region corresponding to a change in the shape of the workpiece; a rendered tool image creation section for rendering a tool image by ray tracing for the current tool rendering region; and an image transfer section for transferring a partial image of the previous tool rendering region and the current workpiece rendering region to be updated from the rendered workpiece image buffer to a display frame buffer as well as transferring the current tool rendering image to the display frame buffer.