Abstract: A method of modular construction of buildings and novel support members for use in such construction utilizing metal base members (2) which are first affixed to a floor or foundation (1) then a series of metal uprights (20) are affixed to said base members by u-shaped connecting member (16). In-fill panels (9) are fixed between said uprights and said base members. A metal flashing (6) is attached to said base member. A channel member (25) connects the top of the said uprights giving support to the building against sideways movement. The said in-fill panels also assist in preventing sideways movement by reason of their spigot-type attachment to said uprights and said base member. The novel support members of the present invention are the channel member (25) and the in-fill panel (9).