We give a brief overview of the analytical solutions for the elastic fields of inclusions in composite solids with an emphasis placed on nanocomposites. Besides, we describe the most popular analytical procedures used in calculations of the elastic fields of inclusions in nanocomposites. These procedures include the Green function method, the method of surface dislocation loops, integration of the equations of equilibrium, and the method of infinitesimal inclusions. Also, we discuss and compare the solutions for the elastic fields of nanoinclusions, derived within linear elasticity, with those obtained using atomistic simulations. With this comparison, it is shown that the linear elasticity approach is valid down to extremely small inclusion dimensions.
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