Disclosed is an automatic tablet packing apparatus having sliding racks, wherein tablets received in a plurality of tablet cassettes are successively packed on a per dose basis based on a medical prescription. Each of the sliding racks includes a pair of left and right partition walls, a tablet discharge passage to guide the tablets discharged from the tablet cassettes being defined by facing inner surfaces of the left and right partition walls. Cassette pedestals are attached to outer surfaces of the left and right partition walls and in turn, the tablet cassettes are detachably arranged on the cassette pedestals. The left and right partition walls are able to be individually pulled out from a body of the apparatus. As the left or right partition wall is pulled out, the tablet discharge passage is revealed to the outside thus enabling easy cleaning thereof.