Compressive strength of a steel hollow pyramid placed onto the open mouth of a steel square tube, which is simply named the steel pyramid-to-tube socket connection, was experimentally investigated. Thirteen specimens were tested with various conditions such as welded or metal-touched between the elements, free or restraint edge of the tube, full-web or open-web of the pyramid, entirely uniform compression or local compression of loading, and normal friction or reduced friction. The ultimate behavior, and consequently, the compressive strength as well as the stiffness of the connection were largely affected by these conditions. The analytical resolution about the effects is not available at present. However, the socket connection with the ordinary condition that the pyramid is welded to the tube and to the lid plate, provides sufficient stiffness and strength for practical use.