Buckling failure is quite a common occurrence in plates under compression, in particular when the plate’s thickness is sufficiently small with respect to others plates’ sizes; such a mode of crisis can often precede strength failure. Buckling failure under tension loading can also be a practical occurrence, especially in cracked plates in which it often takes place as a local buckling phenomenon, due to compression stresses transverse to the loading direction which develop around such imperfections. The aim of the present paper is to analyse the buckling phenomena of variously cracked rectangular elastic thin plates under tension or compression, by considering the effects of various geometrical, mechanical and boundary characteristics of the problem. A short explanation of the buckling phenomena in plates is recalled and several numerical parametric analyses are performed, employing the finite element method, in order to determine the critical load multiplier, in compression or in tension, by varying some of the problem’s geometrical and mechanical parameters. In particular, the buckling critical load multiplier is determined for different crack lengths, crack orientations and material Poisson coefficients and by varying the plate’s boundary conditions. Furthermore, some cracked configurations are analysed by means of a fully geometrical non-linear analysis, with contact between crack faces taken into account, in an effort to understand the effective whole structural behaviour also beyond the critical load. The results obtained are summarised graphically in figures and some interesting and useful conclusions are drawn on the sensitivity to the above-mentioned parameters to the buckling failure of variously restrained cracked compressed or tensioned plates.