Numerical study on buckling of steel web plates with openings numerical study;web plate with openings;elastic and inelastic buckling;buckling stress modification factor; Cellular and castellated steel beams are used to obtain higher stiffness and bending capacity using the same weight of steel. In addition, the beam openings may be used as a pass for different mechanical fixtures such as ducts and pipes. The aim of this study is to investigate the effect of different parameters on both elastic and inelastic critical buckling stresses of steel web plates with openings. These parameters are plate aspect ratio; opening shape (circular or rectangular); end distance to the first opening; opening spacing; opening size; plate slenderness ratio; steel grade; and initial web imperfection. The web/flange interaction has been simplified by web edge restraints representing simply supported boundary conditions. A numerical parametric study has been performed through linear and nonlinear finite element (FE) models, where the FE results have been verified against both experimental and numerical results in the literature. The web plates are subject to in-plane linearly varying compression with different loading patterns, ranging from uniform compression to pure bending. A buckling stress modification factor (${\beta}$-factor) has been introduced as a ratio of buckling stress of web plate with openings to buckling stress of the corresponding solid web plate. The variation of ${\beta}$-factor against the aforementioned parameters has been reported. Furthermore, the critical plate slenderness ratio separating elastic buckling and yielding has been identified and discussed for two steel grades of DIN-17100, namely: ST-37/2 and ST-52/3. The FE results revealed that the minimum ${\beta}$-factor is 0.9 for web plates under uniform compression and 0.7 for those under both compression and tension.