The models for the forecast of elastic characteristics of fibrous composite materials taking into account scale effects is provided in work. For calculations models within the gradient theory of elasticity the method of radial multiplies and generalized Eshelby model is used for the multilayered cylindrical inclusions. To find the analytical solutions for the problem of definition of effective modules of elasticity of composites the generalized Papkovich-Neuber representation is used. The test calculations show significant influence of scale effects on effective characteristics of the studied composites.