The study is devoted to prediction of elastic and creep properties of thermoplastic polymer nanocomposites reinforced with anisodiametric nanoadditives (either carbon nanotubes, CNTs, or montmorillonite clay, MMT) by considering structural hierarchy of the nanocomposites and the nanofillers itself. The nanocomposites analysed have been based on both synthetic and biodegradable thermoplastic polymer matrices (polyethylene, PE, and plasticized starch, PS, respectively) with potential applications in packaging, building/construction and energetics. It has been demonstrated that modulus of elasticity, stress at break as well as stress at yield of the investigated polymer nanocomposites significantly increase upon introduction of a minor amounts of the aforementioned nanofillers into the polymer matrices. Gain in the modulus of elasticity of the investigated PS based nanocomposites has been described by applying the algorithm of stage-by-stage calculation of the elastic constants of the multiphase-systems containing anisodiametric plate-like nanoparticles with complex structure. Change of the modulus of elasticity of the investigated PE based nanocomposites has been described by applying the theoretical model based on micromechanics approach in consideration of distribution quality of CNTs within the polymer matrix. Creep resistance of neat PE and its nanocomposites in the investigated time frame has been described according to the Findley power law, in spite of the fact, that addition of CNTs increases creep rate to some extent, being the consequence of the nanofiller effect on both crystallinity degree of the polymer matrix as well as viscoelastic properties in the interfacial regions.