Cold-formed steel (CFS) channel sections with web holes are being increasingly popular as vertical load-carrying members. Traditional unstiffened web holes can significantly reduce the compression capacity, which limits their size and spacing. Recently, edge-stiffened web holes have gained popularity, particularly in New Zealand. These channels often experience eccentric compression loading due to combined lateral and gravity loads when used as vertical members. However, there's a lack of studies on how CFS channel sections with these web holes perform under such conditions. This research focuses on numerically studying the structural behavior of CFS channel sections with plain webs, unstiffened web holes, and edge-stiffened web holes under eccentric compression loading along both major and minor axes. Finite element (FE) models were developed to simulate these sections, considering material nonlinearity and initial imperfections. The FE analysis results closely matched experimental results in terms of compressive strength and failure modes. The study also investigates how factors like section lengths, thickness, hole size, spacing, and load eccentricities influence the compressive capacity of these perforated channel sections. To account for the effects of the aforementioned design variables on the capacity of these CFS channel members, a combined approach leverages the parametrization of Ansys and the superior solver of Abaqus to conduct a comprehensive parametric study, including a total of 3078 FE models. Based on the FEA results from the parametric study, it appears that the direction of eccentricity (i.e., 𝑒𝑥< 0) emerges as the critical factor affecting the capacity of CFS channel sections with unstiffened or edge-stiffened web holes. Specifically, for 𝑒𝑥 < 0, the compression capacity of the channel section with unstiffened web holes reduced by up to 20.55%, compared to a plain channel section; conversely, the channel section having edge-stiffened web holes had a maximum increase of 20.10%, compared to the same channel with unstiffened web holes. However, when 𝑒𝑥 > 0, the influence of different web openings became less significantly. Finally, based on the FE results of the parametric study, an assessment of current design rules, including American Iron and Steel Institute (AISI-S100) and Australian/New Zealand Standard (AS/NZS-4600), was conducted. The assessment shows the design capacities under eccentric loading predicted by the interaction equation are conservative by 16%-33% on average for plain channels and unstiffened web hole channels. Consequently, new reduction factor interaction equations were proposed for predicting the eccentric compressive capacity of CFS channel sections with different web openings, and a reliability analysis was conducted to ensure the proposed equations could be reliable.