A modular frame system includes a structural member which can take the form of a vertical post or a horizontal beam. The member has a central, generally rectangular tubular body. The tubular body has four sides, two of which are connected by a substantially flat corner part. The member also has four fins extending from the tubular body in different directions for increased rigidity and stability. The fins also support floor, roof or wall panels. Holes are fabricated in the fins such that the member may be stacked on or attached to other similar structural members to create frameworks for buildings.