Pressing of shirts on a shirt-shaped outer inflatable body advantageously takes place with tensioning the shirt in flat form. To achieve a non-round cross-section, in particular, in the trunk section of the outer body, a supporting framework and at least one inner inflatable body are disposed within the outer body, it being possible for the inner body to be supported on the supporting framework and to subject the outer body to pressure from the inside. For such a purpose, the inner inflatable bodies are inflated, in particular, by a higher pressure than the outer inflatable body. It is, thus, possible for the trunk region to be tensioned laterally outward and for the shirt to be pressed in an advantageously flat form. Using the inner bodies avoids raised edges or sharp points in the enclosure of the outer inflatable body. As a result, the shirts can be pressed without creases.