A mobile shredder comprises a truck having a truck body defining an enclosure and including a partition in the enclosure that divides a storage volume from the remainder of the enclosure for storage of shredded material in the storage volume, a single-shaft rotary shredder mounted in the enclosure outside the storage volume, the rotary shredder comprising a rotor having cutters rigidly mounted thereon, a bin lift and dump mechanism operable to transport material to be shredded from outside to inside the enclosure so as to deliver material to the rotary shredder, and a discharge conveyor operable to transport shredded material from the rotary shredder through the partition to the storage volume. The floor of the storage volume can comprise a walking floor, and the enclosure can have rear doors that are openable to allow shredded material to be discharged through the open rear doors when the walking floor is operated.