Abstract: Method for constructing concrete shear core buildings wherein a steel erection structure is built having steel columns and beams. The steel erection structure is made from pre-assembled segments that include the steel reinforcing bar for the concrete shear core. A peripheral steel structure is also constructed and the steel floors are built, cooperatively supported by the steel erection structure and the peripheral structure. Forms are positioned generally about the steel reinforcing bars and at least a portion of the steel erection structure. Concrete is poured in the volume defined by the forms, to build a portion of the concrete shear core. In a preferred embodiment, the steel erection structure and peripheral steel structure proceed approximately seven to nine floors ahead of the concrete shear core, and the concrete shear core is sized to support the completed building without accounting for the additional structural support provided by the steel erection structure.