A lens shape data processing apparatus and a lens grinding machine having the same apparatus in which the lens shape data reading out and the layout setting work for another spectacle lens can be conducted during the lens edge measurement or the grinding process is provided. The lens shape processing apparatus comprises a memory 33 for storing a plurality of lens shape information for the spectacle frame measured by a frame reader 2, a liquid crystal display unit 7 including an image display section 7b for displaying the lens shape based on the lens shape information and an operation contents display section 7c for displaying items for switching a plurality of screens, a plurality of keys corresponding to the items of the operation contents display section 7c, and an arithmetic control circuit 31 for setting the data for grinding an unprocessed lens into a lens shape based on the lens shape information, wherein the keys are used both to switch to a screen for selecting and accessing one of the lens shape information stored in the memory 33, and to access the preceding lens shape information and the next lens shape information or new lens shape information.