In this study, 18 short-column lightweight ceramsite concrete samples were prepared in rectangular stainless steel pipes, which were used for axial pressure performance tests that took the cross-sectional length–width ratio of the rectangular stainless steel pipe (1.0, 1.5 and 2.0), the wall thickness of the steel pipe (3 mm, 4 mm and 5 mm), and the strength grade of the filled concrete (C20 and C30) as the main parameters. Then, the failure patterns, axial load–displacement curve, axial load–strain curve, ultimate bearing capacity and the interaction between the steel pipe and concrete in the specimens were measured. The test results revealed that the short-column concrete specimens in the steel pipes exhibited typical shear failure and “waist-bulging” failure under axial compressive loads. In the elastic stage, the bearing capacity of the specimens was able to reach 65–85% of the ultimate bearing capacity, with the residual bearing capacity essentially reaching 70% of the ultimate bearing capacity. Furthermore, the ultimate bearing capacity of the specimens demonstrated an increase with the rise in the strength grade of the filled concrete, with the thickness of the stainless steel pipe and with the decrease in the length–width ratio of the steel pipe cross-section. The specimens exhibited a distinct hoop effect. As the length–width ratio decreased and the hoop coefficient increased, the ductility coefficient and the strength enhancement coefficient basically displayed an increasing tendency, while the concrete contribution ratio exhibited a decreasing trend.