In this study, flexural characteristics of low-density polyvinylchloride foam core sandwich structures consist of carbon fibre/epoxy facings hybridised with very thin stainless-steel wire mesh sheets were investigated. A comprehensive work was conducted considering the following design parameters: core thicknesses, wire mesh sizes, stacking sequences of wire mesh sheets and support span lengths for flexural tests. During the evaluation of flexural characteristics, experimental ASTM standards (C393, D3039, D7249 and D7250) were utilised. In addition, experimental flexural stiffness values were compared to analytically obtained results. By hybridisation of carbon fibre/epoxy facings with wire mesh sheets, significant improvements in flexural characteristics of sandwich structures were obtained. Besides improving bending behaviour and the larger amount of load-carrying capacity even at the same deflection values, the sandwiches with wire mesh sheets also prevented catastrophic sudden failure, which is the common case for carbon/epoxy/polymer foam core sandwiches. Response surface methodology was applied to evaluate the effects of the design variables on the load capacity of the sandwiches, and optimal solutions were revealed. The developed sandwiches can be good candidates in applications where both high stiffness-to-weight ratio and resistance to sudden failure are desired.