A flexural and membrane model and a failure criterion have been developed to describe the load–deflection response of two-dimensional continuous flexible steel–concrete composite plates. These nonlinear analytical models have a wide range of applicability and are not limited by plate thicknesses, section depth, material properties, or boundary stiffness. Although the analytical models were developed for a particular load configuration, they can be modified to apply equally well to other load configurations.The overall behaviour of the composite plates ranged from flexural to membrane behaviour; and within the ranges of applicability of the models developed for flexural and membrane behaviour, there is good agreement with the test data. The limiting strength of the composite plates is a function of the internal stresses in the steel plates, and is given by the failure criterion which is based on a combined stress state of shear and tension and an extension of the von Mises–Huber–Hencky yield criterion to ultimate. The mean test-to-predicted ratio for the ultimate load was 1.128, with a coefficient of variation of 0.037.The models, together with the failure criterion, allow the design engineer to easily apply a two-load-level design philosophy, consistent with limit states design format, for the design of flexible steel–concrete composite plates. Key words: analysis, composite, concrete, design applications, ductility, energy absorption, flexible, flexural behaviour, membrane behaviour, plates, steel.