This thesis presents new knowledge in the area of plate buckling, which has use in practical applications in the design of aircraft structures, such as wing or fuselage panels and thin-walled civil engineering structures. The focus of the research is on plates that are skew (parallelogram) in planform and the buckling strength gains that arise because of a stiffening effect caused by the acute angle of the plate and the fixity along the plate edges that continuity of adjacent skew plates imposes. A finite element code, ABAQUS, is adopted to compare the buckling strength of plates that are continuous over an infinite number of bays with isolated (non-continuous) plates that have varying magnitudes of rotational restraint applied along the edges. The continuous results, obtained from VICONOPT, are available in the open literature. The results are presented in the form of unique and comprehensive buckling curves. The continuous VICONOPT solutions are verified using a finite element model and the validity of the assumptions used to obtain the VICONOPT results is assessed. The work on skew plates is extended to assemblies of plates that form skew panels of the type typically used in aerospace applications. Buckling calculations are presented for varying magnitudes of orthotropy and skew angles. Analysis of the panel is compared with a plate having the equivalent orthotropic properties and the results compared to closed-form solutions for equivalent rectangular plates. Because modern aircraft wing are generally ^‘swept-back’ and tapered along their length, the resulting plates that make up the panels are not only skew but also tapered in planform. The effect of this taper together with skew is considered and the buckling strength changes that arise because of the stiffening effect of the planform taper assessed. Finally, panels taken from an optimised benchmark wing, are assessed for buckling to ascertain the effect of making simplifying assumptions about the planform geometry of the panels and the consequences of these assumptions on the panel buckling strength.