On the basis of the method steps in time the problem of unsteady creep are formulated for the bending sandwich panels with thin reinforced bearing layers. The weakened resistance of the filler to transverse shears is taken into account in the framework of the Reissner theory. The mechanical behavior of the component materials of the composition of the layers is modeled by the ratio of the nonlinear hereditary Rabotnov theory of creep. It is shown that in discrete moments of time the mechanical condition of such structures are formally described by the defining equations for composite laminated plates of nonlinear-elastic anisotropic materials with known initial states of stress. The linearization of the formulated problem at each time step is carried out by the method of successive approximations. In the case of cylindrical bending the unsteady creep of elongated rectangular composite sandwich panel with weak honeycomb core are investigated. At short-term and long-term loadings of such plates, the analysis is held for the dependence of flexibility on the parameters of the reinforcement bearing layers. It is shown that using the classical theory of bending of layered plates leads to the prediction of an unjustifiably low flexibility of composite sandwich panels, especially under conditions of long-term loading. It was obtained that when the account of weakened resistance of the filler to the transverse shifts, the two different mechanisms of flexural deformation of three-layer plates can be realized: “classic”, when the flexural strain state prevails, and “non-classical”, when the transverse shear of the filler has a main influence on the deflection. In the latter case, in the vicinity of the supported edges of plate the edge effects, describing a shift of the sandwich panels in the cross direction may arise.