Fiber-reinforced polymer (FRP) sandwich structures offer several advantages compared to structures made of traditional materials, such as high specific strength, good corrosion resistance, low thermal conductivity and rapid component installation. In this context, glass fiber-reinforced polymer (GFRP) cell-core sandwiches composed of outer GFRP face sheets, a foam core and a grid of GFRP webs integrated into the core to reinforce shear load capacity are well suited for load-bearing applications in civil engineering i.e. in bridge deck and roof construction. Despite the great potential of these structural concepts, the use of heterogeneous materials in FRP sandwiches results in more complex failure mechanisms compared to conventional structural components and lack of knowledge regarding the prediction of failure modes makes the design of structural components difficult. This is one of the major disadvantages limiting the acceptance of cell-core sandwiches in civil engineering applications. One of the critical failure modes of cell-core sandwich structures is wrinkling in the webs. A great deal of information exists concerning the phenomenon of skin wrinkling failure of sandwich laminates loaded in compression but comparatively little on wrinkling in the webs of sandwich structures where the pure compression loading is complicated by supplementary transverse tension. The purpose of this research is to develop an appropriate model for the prediction of wrinkling in the webs of cell-core sandwich structures. Two new approaches were developed to predict the wrinkling loads of webs. The first approach examines the wrinkling behavior in webs as an in-plane biaxial compression-tension buckling problem according to the rotated stress field theory. In this regard, extensive experimental, numerical and analytical studies were performed to investigate the interaction between the compression and tension stress tensors during the buckling/wrinkling instability phase of GFRP plates and sandwich panels subjected to biaxial compression-tension loading. The investigations demonstrated that the transverse tension in the biaxial compression-tension set-up induced two simultaneous counteracting effects: a stabilizing and a lateral contraction effect. The stabilizing effect tends to push the plate back to the median plane and thereby delays the onset of buckling/wrinkling instability. In contrast, lateral contraction accelerates the bending of the plate, which leads to a significant decrease in buckling/wrinkling loads. In composite plates, the first effect predominates and increases the buckling loads while in sandwich panels the second effect is dominant and decreases the wrinkling loads. Using the second approach, the wrinkling behavior of foam-filled web-core panels was modeled by applying an improved mixed-mode interaction formula in which two approximate models are developed based on the energy method in order to determine the critical loads when the pure shear and bending stresses act independently on the web. The application of both approaches to a real case study, the GFRP cell-core sandwich roof of the Novartis Campus Main Gate Building proved that they are sufficiently accurate to be used as valid tools assisting the optimum design of sandwich structures whereas existing models result in too conservative predictions.