This paper presents GINsim, a Java software suite devoted to the qualitative modelling, analysis and simulation of genetic regulatory networks. Formally, our approach leans on discrete mathematical and graph-theoretical concepts. GINsim encompasses an intuitive graph editor, enabling the definition and the parameterisation of a regulatory graph, as well as a simulation engine to compute the corresponding qualitative dynamical behaviour. Our computational approach is illustrated by a preliminary model analysis of the inter-cellular regulatory network activating Notch at the dorsal-ventral boundary in the wing imaginal disc of Drosophila. We focus on the cross-regulations between five genes (within and between two cells), which implements the dorsal-ventral border in the developing imaginal disc. Our simulations qualitatively reproduce the wild-type developmental pathway, as well as the outcome of various types of experimental perturbations, such as loss-of-function mutations or ectopically induced gene expression.