Business modelling (BM) is being used in commercial organizations of different sizes and industries all over the world as a tool to design, structure and analyse business processes and activities. Hence, advantages of BM can be exploited by public sector institutions (PSIs) as well. Adoption of open source software (OSS) is another phenomenon that started to spread from individual and corporate users to public environment. In Europe, it was successfully done in German municipalities and Swedish police. Moreover, guidelines on OSS public procurement were developed by the group of researchers led by R. A. Ghosh on the base of EU directives on software management. The aim of the current study is to combine two mentioned above tools (BM and OSS adoption) in one practical approach that could be used by municipalities. The main reason for doing this is obvious lack of findings in both theoretical and practical aspects though the subject is being broadly discussed and promoted. The overall purpose of the current research is to design an OSS based business model for Kivos municipalities that can be later generalized to other public organizations, probably even in other countries. The specific feature of this business modelling is that it is created upon value and relationships instead of issues related to money which is more common for BM. The current study is an exploratory and inductive qualitative research where case study was chosen as a research strategy. Data collection was conducted using the following techniques: literature review – for secondary data collection, and communication (interview and survey) – for primary data collection. Theoretical framework includes literature (sources providing both general and specific information related to the subject of interest. All gathered information was interpreted and analysed through the instrumentality of enterprise modelling or simply summarised and discussed verbally. On the base of interpreted results of theoretical and empirical studies desired OSS based business relationships model was designed and described for Kivos municipalities. It is based on value which in particular case implies sharing information, knowledge and experience as well as mutual assistance and reliable interaction between participants of relationships existing in OSS environment.