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Steel plates play a pivotal role in the construction of different types of structures used in civil engineering. According to Eurocode 3, plated structures may be designed using three different approaches: the effective width method, the reduced stress method, and the finite element analysis. For the particular case of elements under stress gradients, the effective width method utilises the local buckling coefficient of a plate to calculate the effective cross-sectional area for structural elements. Since the effective width method was developed for uniform web and flange panels, Eurocode 3 and most design codes have no specific provisions for the particular case of non-rectangular panels, stating that they may conservatively be treated as rectangular panels with larger width. With the final objective of improving design rules for tapered members, this paper presented an extensive numerical analysis to evaluate the elastic local buckling behaviour of trapezoidal plates with simply supported end conditions under stress gradients. The study identifies the relative importance of several parameters that influence the local buckling coefficient, such as the tapering ratio of the panel, normalized plate length, and stress ratio. Numerical results are used to propose approximate closed-form expressions that can be used to compute the local buckling coefficient for trapezoidal plates in a direct way. The results show that the proposed formula offers a significant improvement over current Eurocode 3 and most design codes.