A mathematical model of the skeletogenesis and the influence of the physical environment on the morphogenesis of a branching sponge, for example, Haliclona oculata or Lubomirskia baikalensis, is presented. In the model, we assume that the radiate accretive growth process is nutrient limited. With this model we can generate in a simulated accretive growth process branching objects with a similarity to the branching sponges.