A cell's morphology is intricately regulated by microenvironmental cues and intracellular feedback signals. Besides biochemical factors, cell fate can be influenced by the mechanics and geometry of the surrounding matrix. The latter point was addressed herein, by studying cell adhesion on two-dimensional micropatterns. Endothelial cells were grown on maleic acid copolymer surfaces structured with stripes of fibronectin by microcontact printing. Experiments showed a biphasic behaviour of actin stress fibre spacing in dependence on the stripe width with a critical size of approx. 15 μm. In a concurrent modelling effort, cells on stripes were simulated as droplet-like structures, including variations of interfacial energy, total volume and dimensions of the nucleus. A biphasic behaviour with regard to cell morphology and area was found, triggered by the minimum of interfacial energy, with the phase transition occurring at a critical stripe width close to the critical stripe width found in the cell experiment. The correlation of experiment and simulation suggests a possible mechanism of the cytoskeletal rearrangements based on interfacial energy arguments.