Buckling of a heavy standing plate with top load

Buckling of a standing plate subjected to self weight and top load is studied. The vertical sides are simply supported and Levy separation yields an ordinary differential equation that is integrated by an accurate, efficient initial value method. Exact and asymptotic formulas are also found. The effects of self weight and top load both contribute to the buckling. Their contributions are not linear. For narrow plates, if top load dominates it does not matter whether an end is clamped or simply supported. If self weight dominates, the buckling of a narrow plate only depends on the bottom condition.