We study the existence of propagating mode-I fracture in amorphous materials using atomistic models. We used the continuous random network (CRN) model for creating the amorphous sample, using a perfect 2D-analogy for the famous WWW (Wooten, Winer & Weaire) Monte-Carlo algorithm, for creating high-quality CRN's. For modeling fracture, a 2D initial-value molecular-dynamics simulations was run on the amorphous sample. The results of our simulations reproduce all the main features of the experiments. Besides achieving a steady-state crack under a constant driving displacement (which would not achieved so far by any other atomistic model for amorphous materials), we get a clear micro-branching instability, with macro-branching for larger drivings. Beside the qualitative visual similarity of the simulated cracks to the experiment, we also reproduced the experimentally observed oscillations of the crack-velocity, occurring when micro-branching starts to appear.