This contribution deals with the modelling and analysis of stability problems for thin composite annular plates interacting with elastic heterogeneous subsoil. The object of analysis is an annular plate with a deterministic heterogeneous microstructure and the apparent properties smoothly varying along a radial direction. The aim of contribution is to formulate two macroscopic mathematical models describing stability of this plate. The considerations are based on a tolerance averaging technique. The general results are applied to the analysis of some special stability problems. The obtained results of critical forces with those obtained from finite element method are compared.