Different lots of Tilsit cheeses, which are characterized by their open structure caused by pressing under their own weight during manufacture, were subjected to uniaxial compression, a quasi‐standard for the evaluation of mechanical properties of hard and semi‐hard cheeses. Additionally, video films showing the behaviour of the specimens during compression were analysed. For standard Tilsit with a fat content of 35% in dry matter, the cheese mass proved to be highly anisotropic with respect to stress response and lateral expansion expressed as apparent Poisson number. Specimens cut perpendicular to the flat side of the cheese wheels, which had lentil‐shaped eyes with their major axis parallel to the compression plates, showed significantly higher stresses and lower Poisson numbers than specimens sampled parallel to the flat side of the cheese wheels. Therefore, stress values calculated on the basis of actual specimen diameter were different from those calculated by assuming constant specimen's volume. However, for samples with a fat content of approx. 60% in dry matter no differences caused by compression direction were observed.