A tough, water-proof building system provides wall, ceiling, and floor structures, as well as accessories. The walls can be designed to have vertical and horizontal strengths sufficient to be used in place of concrete, as an engineered solution, both above grade and below-grade, including in severe weather conditions. Walls have inner and outer layers, and structurally reinforcing members extending, typically as a layer and/or stud, the full height of the wall, at spaced locations along the length of the wall. The spaces between the structurally reinforcing members are optionally filled with insulating foam. An optional reinforcing stud is attached to, or overlaid by, the inner layer, and extends inwardly into the building from what is otherwise the inner surface of the building panel/wall panel. A building floor can be supported from the load-bearing wall, at locations on the floor support members which are below the top of the load-bearing wall.