Glass Network is a class of gene regulatory networks used to model the interactions and controls existing among molecules, proteins and other transcription factors in a biological system. The activities of the genes and their regulatory effects are controlled through their concentration levels defined by threshold functions which are only defined at off threshold value. Qualitative and numerical studies of this network have revealed a lot of properties such as existence of periodic orbits, stable oscillation, chaos and steady states. This study applied the method of geometric singular perturbation to investigate the behaviour of the system within the threshold neighbourhood (known as singular states) of the networks. Some results such as transparency condition on non-sliding walls and manifold of sliding walls were obtained.