Many researches have confirmed that the dynamic increase factor (DIF) of concretelike materials in compression measured by split Hopkinson pressure bar (SHPB) includes considerable structural effects, which do not belong to strain-rate effect. It has been found that the factors responsible for structural effects include material parameters (i.e. hydrostatic dependence, dilation parameter), specimen geometry (i.e. diameter), end interface friction and material inertia. However, their intrinsic relations have never been fully clarified. Based on two well-established material models (extended Drucker-Prager model in Abaqus and the Concrete Damage Model Release III in LS-DYNA), this paper uses numerical SHPB tests to investigate the interactive relations among these structural factors. It was found that the lateral confinement in a SHPB specimen is responsible for all structural effects in a SHPB test of concrete-like material. Two independent mechanisms can produce the lateral confinement, i.e. (i) friction on the interface of SHPB specimen and pressure bars, which prevents the expansion of the SHPB specimen during compression, and (ii) lateral inertia in SHPB specimen, which generates reactive radial confinement stress. Dilation can further enhance DIF, but it has to interact with either or both mechanisms. The ways that various structural factors contribute to structural effects through these mechanisms are clarified.