Abstract: A cutting machine for solid bodies such as rubber tires according to the invention comprises a blade base 14 moved vertically by pressing cylinders 1. Downwardly directed cutting blades 18 are mounted on the underside of the blade base 14. These blades 18 can retractably project through slits 15a formed in a presser plate 15 positioned below the blade base 18. Rubber tires T.sub.1 placed on a receiver 27 are cut by the blades 18 with the presser plate 15 compressively retaining the tires T.sub.1. The resultant cut pieces are discharged by horizontally moving an accommodating box 22 through discharge cylinders 23. The receiver 27 is slightly rotated after a predetermined number of cutting operations.