The bodies of Matheon are: General Assembly, Council, Executive Board, and Chair. Chair, Council, and Executive Board are elected by the General Assembly.

The Chair represents Matheon and is responsible for the management of the current business. He/She is being assisted by the Deputy Chair.

The Central Management Unit supports the Chair and all Matheon members. It consists of a financial administrator, an officer for European Joint Research Initiatives, an assistant to the Executive Board, a press officer, a web-administrator and a person responsible for the school activities

The Executive Board meets several times per year and is responsible for the scientific program of Matheon, for the reporting of its results and for the budget.

The Council gives advice concerning the scientific program and coordinates and leads the activities of the individual Application Areas and Mathematical Fields.

The General Assembly includes all the members of Matheon and elects Chair, Council and Executive Board.

The Scientific Advisory Board gives advice in scientific, technological, and organizational matters, for instance with a view to national and international cooperations and contacts to industry.