Despite the efforts made towards the Millennium Goals targets during the last decade, access to improved Water Supply or basic Sanitation remains still not accessible for millions of people across the World. This paper proposes a set of models that use 25 key variables from the WatSan4Dev dataset and country profiles involving Water Supply and Sanitation (Dondeynaz et al 2012). This paper proposes the use of Bayesian Network modelling methods because adapted to the management of non-normal distribution, and integrate a qualitative approach for data analysis. They also offer the advantage to integrate preliminary knowledge into the probabilistic models. The statistical performance of the proposed models ranges between 80 and 95% which is very satisfactory taking into account the strong heterogeneity of variables. Probabilistic scenarios run from the models allow a quantification of the relationships between human development, external support, governance aspects, economic activities and Water Supply and Sanitation (WSS) access. According to models proposed in this paper, a strong poverty reduction will induce an increment of the WSS access equal to 75-76% through: 1) the organisation of on-going urbanisation process to avoid slums development; and, 2) the improvement of health care for instance for children. On one side, improving governance, such as institutional efficiency, capacities to make and apply rules or control of corruption will also have a positive impact on WSS sustainable development. The first condition for an increment of the WSS access remains of course an improvement of the economic development with an increment of household income. Moreover, a significant country environmental commitment associated with civil society freedom of expression constitutes a favourable environment for sustainable WSS services delivery. Intensive agriculture through irrigation practises also appears as a mean for sustainable WSS thanks to multi-uses and complementarities. Strong and structured agriculture sector facilitates rural development in areas where WSS access often steps behind compared to urban areas . External financial support, named Official Development Aid (ODA), plays a role in WSS improvement but comes last in the sensitivity analyses of models. This aid supports first poor countries at 47%, and is associated to governance aspects: 1) political stability and 2) country environmental commitment and civil society degree of freedom. These governance aspects constitute a good framework for aid implementation in recipient countries. Modelling is run with the five groups of countries as defined in Dondeynaz et al 2012. Models for profile 4 (essential external support) and profile 5 (primary material consumption) are specifically detailed and analysed in this paper. For countries in profile 4, to fight against water scarcity and desertification pressure should be the priority. However, for countries in profile 5, efforts should first concentrate on political stability consolidation while supporting economic activity diversification. Nevertheless, for both profiles, reduction of poverty should remain the first priority as previously indicated.