The punching shear failure of reinforced concrete (RC) flat slabs is an undesirable type of failure, as it is sudden and brittle. This paper presents an experimental and numerical study to explore the behavior of flat slabs made of different types of concrete under the influence of punching shear. Experimental tests were carried out on four groups of flat slabs, each group representing a different type of concrete: ordinary normal concrete (NC), high-strength concrete (HSC), strain-hardening cementitious composite concrete (SHCC), and ultra-high-performance fiber concrete (UHPFC). Each group consisted of six slabs, one representing an unreinforced control slab other than the reinforcement of the bottom mesh, and the others representing slabs internally reinforced with SHCC-filled steel tubes and high-strength bolts. An analytical equation was used to predict the punching shear capacity of slabs internally reinforced using steel assemblies. A numerical model was proposed using the ABAQUS program, and was validated by comparing its results with our experimental results. Finally, a case study was performed on large-scale slabs. The results showed that using steel assemblies inside NC slabs increased the slab’s punching shear capacity but does not completely prevent punching shear failure. Internally unreinforced slabs made of UHPFC and SHCC were able to avoid punching shear failure and collapse in a ductile bending pattern due to the high compressive and tensile strength of these types of concrete. The proposed analytical method succeeded in predicting the collapse load of slabs reinforced with steel assemblies with a difference not exceeding 9%.