The problem of the buckling under bi-axial compression is considered for flat rectangular isotropic plates with simple edge conditions and no lateral restraint. The buckling stress coefficient is plotted against the side ratio for various conditions of edge restraint and a known compression or tension on the sides of the plate. It is found that there is some reduction in the buckling stress if the sides of the plate are subjected to compressive stresses and, conversely, there is an increase for tensile stresses. Furthermore, for plates with large side ratios, there is a rapid decrease of the spanwise buckling stress as the chordwise compressive stress approaches its appropriate Euler instability value.