The Arbitration Board has a presidium composed of a chair, a deputy chair and a third member. In addition, 17 alternates have been appointed as set out in the statutes of the Arbitration Board. The members of the Presidium and the alternates are either supreme court judges or high court judges (named below), and they have all been appointed by the president of the Supreme Court. A number of technical arbitrators with expertise in the field of building and construction are also attached to the Arbitration Board.

An arbitral tribunal usually has three members, a legal arbitrator and two technical arbitrators, but in some cases there are five members and in others just one. If the arbitral tribunal set up by the Arbitration Board has more than one member, the chair of the Presidium will select the presiding arbitrator from among the members of the Presidium and its alternates. The presiding arbitrator is thus a legal arbitrator.

If a case is to be heard by one arbitrator only, the arbitrator may be either a legal or a technical arbitrator. The Arbitration Board appoints technical arbitrators specifically for individual cases on the basis of the subject matter of the dispute to be resolved. This applies irrespective of whether the tribunal has one technical arbitrator or two technical arbitrators in a tribunal with three or five arbitrators. When selecting the technical arbitrators, the Arbitration Board attaches importance to criteria such as professional qualifications, experience and suitability for the dispute in question.

In special cases, the chair of the Presidium may select one or more current or former supreme or high court judges or other people with a background in law who meet the conditions to be appointed arbitrators. The chair also decides who is to be the presiding arbitrator.