The shape transition of a one-layer thick strained island deposited on a semi-infinite substrate has been theoretically investigated from an energy variation calculation. It is found that depending on the misfit strain, the initially circular island may become unstable beyond a critical size and can evolve toward an elliptical shape. As the surface of the island increases, another transition is expected to occur which consists in the ellipse splitting into two identical circular islands of smaller size. A shape diagram is finally displayed for the island as a function of the misfit strain and island surface and a scenario of nanostructure evolution is discussed. (C) 2017 Elsevier B.V. All rights reserved.