A possible mechanism for cross-tie fibril generation in crazes of amorphous polymers is proposed. Detailed finite element calculations are performed on an axisymmetric model of a single fibril inside the craze. These calculations suggest that the hydrostatic stress inside the fibril is large enough to cause cavitation and subsequent growth of initial imperfections inside the fibril. The calculations demonstrate that these cavities will then grow by local plastic flow around them, leading to a continuous network of main fibrils interconnected by cross-tie fibrils.