A staining apparatus for staining of tissue specimens placed on microscope slides comprises a number of staining stations (4) and other working stations (1, 2, 3), where the staining stations (4) receive vessels (5) having liquid baths for receiving baskets containing microscope slides with the topical specimens, and a transport mechanism (17-20) having a hoisting device (17) arranged to be moved over the vessels (5) and to place baskets in or take these up from the vessels, and to transfer the baskets between the working stations (1-4) in accordance with a programme-controlled staining process. The vessels (5) are transparent and are arranged in a number of horizontal rows placed above one another on a stepped base like a tribune, the tribune having a gradient allowing visual inspection of the individual vessels (5) at the working stations (4) from a place of view in front of the apparatus.