This paper aims to analytically study the effect of loading conditions and confinement type on the mechanical properties of the concrete-steel composite columns under axial compressive loading. The axial loading is applied to the composite columns in the two ways; only on the concrete core, and on the concrete core and steel tube simultaneously, which are called steel tube-confined concrete (STCC) and concrete-filled steel tube (CFST) columns, respectively. In addition, the confinement is investigated in the three types of passive, short-term active and long-term active confinement. Nonlinear finite element 3D models for analyzing these columns are developed using the ABAQUS program, and then these models are verified with respect to the recent experimental results reported by the authors on the STCC and CFST columns experiencing active and passive confinements. Axial and lateral stress-strain curves as well as the failure mode for qualitative verification, and compressive strength for quantitative verification are considered. It is found that there is a good consistency between the finite element analysis results and the experimental ones. In addition, a parametric study is performed to evaluate the effect of axial loading type, prestressing ratio, concrete compressive strength and steel tube diameter-to-wall thickness ratio on the compressive behavior of the composite columns. Finally, the compressive strength results of CFST specimens obtained via the finite element analysis are compared with the values specified by the international codes and standards including EC4, CSA, ACI-318, and AISC, with the results showing that ACI-318 and AISC underestimate the compressive strength of the composite columns, while EC4 and CSA codes present overestimated values.