A smal-size apparatus for sorting sheets or the like can form a delivery route by repeating sorting operation and prevent an overflow of sheets or the like. To this end, auxiliary sorting compartments are provided in an accumulator means in the sorting operation for the first time, and when an overflow occurs, the allocated sorting compartments are shifted each by one compartment to the side of the auxiliary sorting compartment. In the first-time sorting operation, destination codes and thicknesses are stored in memory, and by the destination codes and thicknesses stored, overflow is predicted, a plurality of sorting compartments are allocated. By this arrangement, the sheets or the like can be prevented from overflowing, so that those sheets or the like which are rejected need not be manually added afterwards, and the efficiency of the sorting work can be improved.