The popular analytical and numerical models to residual stresses and distortions in composite structures during curing are reviewed with emphases being placed on the numerical models with viscoelastic, path-dependent, CHILE constitutive laws, and corresponding numerical implementation into finite element analyses in this paper. A simple C-section composite part made of AS4/8552 prepreg, which has been investigated previously, was taken as an example to compare the difference in residual stresses and distortions with analytical model and numerical method with different constitutive laws. This paper mainly focuses on the effects of residual stresses generated at the different stages during curing on the finial distortions of composite structures for different constitutive laws, especially for effects of residual stresses generated in the rubbery stage on the final distortions. The results show that there is insignificant difference in the calculated residual stresses and distortions in C-section composite part induced during curing with different constitutive laws except the CHILE() law.