A method for constructing a multi-story building, comprising: constructing a foundation to support walls (A, B) of the multi-story building, including a plurality of mating anchors (1111A-1111D) embedded in the foundation , each mating anchor (1111A-1111D) having a top protruding from the foundation ; assembling a plurality of wall trusses (1- 4), each consisting of a plurality of vertical members (101 - 105), adjacent ones of which are interconnected at the top and bottom by horizontal beams (111 - 114, 121 - 124), spanning the space between adjacent vertical members and connected to a respective side of the vertical members, wherein at least two vertical members at each end of the wall truss comprise hollow members; affixing the bottom of a set of wall trusses to the foundation by setting the bottom of the hollow members of the vertical members (101 - 105) of a set of wall trusses over the protruding top of the mating anchor (1111A-1111D) embedded in the foundation ; for each floor of the multi-story building: inserting a mating member (341-350) into the top of the hollow columns of at least two of the vertical members for each wall truss, where the mating member protrudes above the top of the hollow column in which it is inserted; and stacking additional wall trusses on top of the existing wall trusses installed for the floor below, by inserting the protruding top of the mating member of the vertical members into the bottom of the hollow columns of the additional wall truss. constructing a foundation to support walls (A, B) of the multi-story building, including a plurality of mating anchors (1111A-1111D) embedded in the foundation , each mating anchor (1111A-1111D) having a top protruding from the foundation ; assembling a plurality of wall trusses (1- 4), each consisting of a plurality of vertical members (101 - 105), adjacent ones of which are interconnected at the top and bottom by horizontal beams (111 - 114, 121 - 124), spanning the space between adjacent vertical members and connected to a respective side of the vertical members, wherein at least two vertical members at each end of the wall truss comprise hollow members; affixing the bottom of a set of wall trusses to the foundation by setting the bottom of the hollow members of the vertical members (101 - 105) of a set of wall trusses over the protruding top of the mating anchor (1111A-1111D) embedded in the foundation ; for each floor of the multi-story building: inserting a mating member (341-350) into the top of the hollow columns of at least two of the vertical members for each wall truss, where the mating member protrudes above the top of the hollow column in which it is inserted; and stacking additional wall trusses on top of the existing wall trusses installed for the floor below, by inserting the protruding top of the mating member of the vertical members into the bottom of the hollow columns of the additional wall truss. inserting a mating member (341-350) into the top of the hollow columns of at least two of the vertical members for each wall truss, where the mating member protrudes above the top of the hollow column in which it is inserted; and stacking additional wall trusses on top of the existing wall trusses installed for the floor below, by inserting the protruding top of the mating member of the vertical members into the bottom of the hollow columns of the additional wall truss. <EOS>