Sandwich panels comprise a thick, light-weight plastic foam such as polyurethane, polystyrene or mineral wool sandwiched between two relatively thin steel faces. One or both steel faces may be flat, lightly profiled or fully profiled. Until recently sandwich panel construction in Australia has been limited to cold-storage buildings due to the lack of design methods and data. However, in recent times, its use has increased significantly due to their widespread structural applications in building systems. Structural sandwich panels generally used in Australia comprise of polystyrene foam core and thinner (0.42 mm) and high strength (minimum yield stress of 550 MPa and reduced ductility) steel faces bonded together using separate adhesives. Sandwich panels exhibit various types of buckling behaviour depending on the types of faces used. Three types of buckling modes can be observed which are local buckling of plate elements of fully profiled faces, flexural wrinkling of flat and lightly profiled faces and mixed mode buckling of lightly profiled faces due to the interaction of local buckling and flexural wrinkling. To study the structural performance and develop appropriate design rules for sandwich panels, all these buckling failure modes have to be investigated thoroughly. A well established analytical solution exists for the design of flat faced sandwich panels, however, the design solutions for local buckling of fully profiled sandwich panels and mixed mode buckling of lightly profiled sandwich panels are not adequate. Therefore an extensive research program was undertaken to investigate the local buckling behaviour of fully profiled sandwich panels and the mixed mode buckling behaviour of lightly profiled sandwich panels. The first phase of this research was based on a series of laboratory experiments and numerical analyses of 50 foam-supported steel plate elements to study the local buckling behaviour of fully profiled sandwich panels made of thin steel faces and polystyrene foam core covering a wide range of b/t ratios. The current European design standard recommends the use of a modified effective width approach to include the local buckling effects in design. However, the experimental and numerical results revealed that this design method can predict reasonable strength for sandwich panels with low b/t ratios (< 100), but it predicts unconservative strengths for panels with slender plates (high b/t ratios). The use of sandwich panels with high b/t ratios is very common in practical design due to the increasing use of thinner and high strength steel plates. Therefore an improved design rule was developed based on the numerical results that can be used for fully profiled sandwich panels with any practical b/t ratio up to 600. The new improved design rule was validated using six full-scale experiments of profiled sandwich panels and hence can be used to develop safe and economical design solutions. The second phase of this research was based on a series of laboratory experiments and numerical analyses on lightly profiled sandwich panels to study the mixed mode buckling behaviour due to the interaction of local buckling and flexural wrinkling. The current wrinkling formula, which is a simple modification of the methods utilized for flat panels, does not consider the possible interaction between these two buckling modes. As the rib depth and width of flat plates between the ribs increase, flat plate buckling can occur leading to the failure of the entire panel due to the interaction between local buckling and wrinkling modes. Experimental and numerical results from this research confirmed that the current wrinkling formula for lightly profiled sandwich panels based on the elastic half-space method is inadequate in its present form. Hence an improved equation was developed based on validated finite element analysis results to take into account the interaction of the two buckling modes. This new interactive buckling formula can be used to determine the true value of interactive buckling stress for safe and economical design of lightly profiled sandwich panels. This thesis presents the details of experimental investigations and finite element analyses conducted to study the local buckling behaviour of fully profiled sandwich panels and the mixed mode buckling behaviour of lightly profiled sandwich panels. It includes development and validation of suitable numerical and experimental models, and the results. Current design rules are reviewed and new improved design rules are developed based on the results from this research.