A tough, water-proof building system, and methods of making the system elements and constructing buildings, which provides wall, ceiling, and floor structural panels and corresponding walls, ceilings, and floors,. 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, such that no concrete need be used except for floor slabs. Panels have inner and outer layers, and structurally reinforcing members. Structurally-reinforcing members extend, typically as a layer and/or stud, the full height of a wall, at spaced locations along the length of the wall. Spaces between the structurally reinforcing members are optionally filled with rigid 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.