Unsymmetrical sections are commonly used in thin-walled metal structures for the optimal utilization of materials and fast production. The members with these sections are usually slender and susceptible to lateral-torsional or flexural-torsional buckling, and furthermore, their structural behaviors are often complex because the shear center doesn't coincide with the centroid. Although conventional warping beam-column elements can simulate these buckling modes, they are derived based on the assumption of a doubly-symmetric section. It would be unreliable for to use these conventional elements when evaluating the buckling strength of an unsymmetrical slender section. Against this background, a refined warping beam-column element for unsymmetrical sections is derived by the authors and implemented within the educational structural analysis software MASTAN2 (v4.0). This paper reviews the essential theory and the development of element formulations with several benchmark examples that demonstrate accurate results from the proposed numerical framework. These examples are also analyzed by the conventional warping elements for assessing the impact of modeling members of unsymmetrical sections as doubly symmetric.