Anabranching rivers are formed of islands of various shapes and this study applies a variational analytical approach to explain the morphology of islands of a particular basic shape. A theoretically modeled anabranching river is developed based on observations from the middle and lower Yangtze River, which alternates between a single channel and a two-channel anabranching reach with islands approximately triangular in planform such that one anabranch is longer than the other. The equilibrium condition of the model river is derived from a variational investigation of basic relationships of flow continuity, channel boundary resistance, bedload transport, and energy conservation in the anabranching river. We demonstrate that when such a system reaches stationary equilibrium the triangular planform of the island is determined by the proportions of water and sediment passing through the two channels. We also show that the shorter straight channel takes a larger proportion of sediment relative to its proportion of water. For the island to take a streamlined morphology, the difference between the proportions of water and sediment discharge entering each channel needs to be as small as possible. When the paired proportions of water and sediment discharge take different values, the streamlined morphologies of the island vary in a wide range. In comparison with the measured morphologies of the five islands located in the middle-lower Yangtze River, the theoretically determined lengths of the islands are remarkably consistent, varying from the corresponding field measurements by a range of <±10%.