The proper modelling of sandwich panels with high inhomogeneity of material properties through-thickness relies mostly on the application of structural models with layerwise descriptions. This work provides an assessment of layerwise finite element models, with various through-thickness expansions of displacements, aimed for supersonic flutter analysis of viscoelastic sandwich panels. The proposed layerwise models make use of not only shear deformation plate theories devoid of thickness stretching, but also further refined kinematic models, with quasi-3D predictive capabilities, based on Lagrange z-expansions with thickness stretching. To describe the pressure generated by the supersonic airflow, the well-established First-order Piston Theory is applied as aerodynamic model. Numerical applications of sandwich panels include either viscoelastic or purely elastic core with skins made of metal or laminated composite, using unidirectional or curvilinear fibres. The panels considered are thin or moderately thick, with core thickness ratios ranging from narrow to wide cores, and with either simply supported or clamped boundary conditions. Overall, it is concluded that when dealing with thin plates, the layerwise model involving the First-order Shear Deformation Theory (FSDT), without thickness stretching, ensures a fair compromise between numerical accuracy and computational effort on supersonic flutter analysis of soft core sandwich panels, with either viscoelastic or purely elastic core. In addition, the impact of various design parameters (e.g. boundary conditions, core thickness ratio and core loss factor) on the aeroelastic flutter response is examined.