This paper presents an analytical model to investigate the static behaviour of sandwich plates comprised of two isotropic face sheets and a honeycomb core. Through-thickness transverse shear stresses were considered using a unified displacement field with which various plate theories were implemented, i.e., exponential, third-order, hyperbolic, sinusoidal, fifth-order, Mindlin, and the classic plate theory. The equilibrium equations of a simply-supported sandwich panel were derived using the principle of virtual work and Navier solution was obtained under static transverse loading. After validating of the model, various mechanical and geometrical parameters were varied to characterise the behaviour of the structure under regular and auxetic response. It was found that the auxeticity of the core strongly affects the mechanical response, e.g., in controlling deflection, in-plane anisotropy, and Poisson’s ratio. Cell wall angle was found to be most critical parameter that can be used to adjust anisotropy, out-of-plane shear modulus, transverse shear stress distribution, and deflection of the panel. Also the cell aspect ratio controls the sensitivity of the core response to other geometrical variations. In terms of the higher-order theories, the deflection-dependent parameter of the unified formulation seems to have more control of maximum deflection compared to independent rotations. Auxeticity of the core showed some benefits in controlling anisotropy, deflection and providing additional out-of-plane shear rigidity. Overall, since there is not one-to-one relationship between specific values of Poisson’s ratio, anisotropy, and shear rigidity, careful design considerations must be invested to obtain a correct mechanical response.