Abstract: Heterogeneous composite material in the context of elasticity at finite deformation was studied by the method of internal homogenization analysis. In the process of research, the multiscale finite mechanism was introduced and the heterogeneous composite material was taken as a non-local representative volume element(RVE). The interval effective quantities such as tangent tensor, first Piola-Kirchhoff stress and strain energy were obtained by using a multiscale finite element strategy combined with the improved particle swarm optimization algorithm, with full consideration of the internal parameter uncertainty of RVE set in different deformation-controlled boundary conditions and the effect of different internal conditions on the interval effective quantities of the RVE.