Abstract Two models are derived to predict the plastic zone size near a crack in a ductile layer sandwiched by two rigid substrates when the size is larger than the layer thickness. To examine the validity, the results are compared with the one’s of finite element analysis. As a result, it is found that for the mode mixity of φ<15° the modified Dugdale’s model and modified Irwin’s model give over-estimation of the plastic zone size, while for φ≥30° those give an upper and lower limit, respectively. The effect of constraint by the rigid substrates upon the plastic zone size can be represented by elastic properties of the substrates and the layer material. The effects of several factors such as the magnitude of load scaled by K ∞, mode mixity φ, and T-stress are explored.