B El kechebour - University of Sciences and Technology Houari Boumediene (USTHB), Faculty of Civil Engineering, Bab Ezzouar, Algiers, Algeria.

The aim of this study is to present software that permits the dimensioning of an urban densification. The model is based on the modeling of the functions and the corresponding spaces into an orthogonal parcel having a planar form. The elaboration of this tool is a response to a demand from the Department of the Housing and the Urbanism, which wants mastering the sustainable urban development.The study begins by the identification of the urban functions and their correlations with the urban space. The summation of all spaces that compose the parcel defines the total area called plot area. The space of road into the system is a correlation of the shape, and of the disposition of the plots, and of the number of plots into the Plan. The urban composition is characterized by a mathematical system composed by two equations represented respectively by the urban density and the site coverage ratio. This system is undetermined because there is one unknown quantity: the total plot surface that depends of the road surface. To solving this problem, it is demanded to use the finite difference method.Finally, the work ends by the presentation of the graphs illustrating the urban characteristics and the demonstration of software

densification, functions, spaces, model, characteristics, software