ABSTRACT Cell monolayers on culture dishes were divided into two groups: tensile monolayers and non-tensile ones. In the development of an epithelium, a non-tensile cell monolayer turns into a tightly bound tensile one. Detection of these states was carried out by using the boundary shortening procedure, a computer-based geometrical method to show how much the polygonal cell boundary contracts. Non-tensile monolayers were divided further into two groups according to their motility: a fluctuating monolayer in which cells move laterally, and a stable monolayer in which cells are immobilized. Quantitative determination of cell motility was performed by analysing timelapse cellular patterns. These computer-based geometrical analyses enabled us to divide monolayers into three groups: tensile stable monolayers, non-tensile stable monolayers and fluctuating monolayers, and this study therefore gives an insight into the way in which changing conformations of cells may be assayed.