A sample processing apparatus comprising: a plurality of sample processing units, each processing a sample contained in a sample container; a transport apparatus that transports a sample rack holding a sample container to at least any one of the plurality of sample processing units; a rack feeding section that receives a sample rack and feeds the received sample rack to a transport line of the transport apparatus; and a controller configured to instruct the transport apparatus, according to a quantity of sample racks received by the rack feeding section, to transport a sample rack fed by the rack feeding section to either (a) a sample processing unit which can accept a subsequent sample rack more rapidly than any other sample processing unit or (b) a sample processing unit having a lower processing load than any other sample processing unit. Also, a sample rack transporting method.