Concrete and steel have different advantages, concrete has high compression strength and low cost while steel has high tensile strength, rigidity and ductility. Composite members have other beneficial qualities beside all of them. Composite columns are used extensively in modern buildings essentially in industrial buildings. The main purpose of this study is an analysis and a comparison between the responses (load‐displacements) of different types of composite columns under cyclic loads. For this purpose, a three‐dimensional (3D) finite element model is developed for the columns, the finite element analysis of composite columns is carried out by using ANSYS code. The numerical model considers the elasto‐plasticity of materials and the non‐linearity of contact friction. It is interesting to observe a large ductility of these composite elements and the efficiency of some types of the composite columns than others. The aim of the study is to analyze the encased composite columns under cyclic loads focused on the different type of steel section. The parameters studied are the influence of axial load levels, skeleton curve, ductility, energy dissipation and the peak lateral load also carried out. The results indicate that the first columns of the specimens have a low specimen energy dissipation due the durability of the columns is higher than the axial load applied, and for better ductility and energy dissipation the axial load level of fully encased composite columns should be limited to approximately a value of 0.6.