The stress state of modified composite materials reinforced with whiskered fibers is investigated for the case of uniaxial tension. The modified composite material includes fibers that are a multiphase material, so the composite material composes of three phases: а) base fiber, б) bristled interphase layer is grown on top of the surface of fiber, в) matrix. The stress state in each phase of such a fiber composite material is studied. Two types of fiber composite material consisting of a matrix are considered. The first type is a basic carbon fiber T-650 coated with an interphase layer, where the interphase layer contain carbon nanotubes and epoxy matrix. The second type is a basic carbon fiber IM7 coated with an interphase layer, where the interphase layer contain zinc oxide nanowires and epoxy matrix. The stress state in each of the phases of the modified fibrous composite is examined to evaluate the strength and to compare the strength characteristics of the modified composite with the strength characteristics of the classical composite material consisting of carbon fibers and an epoxy matrix. The study was conducted in several stages. First, effective properties of interphase layers formed by a matrix filled with whiskers or nanotubes were determined. Interphase layers have cylindrical isotropy. As a result, the fibrous composite is considered as a composite system with a transversely isotropic property in each phase: fiber and interphase layer are transversely isotropic, matrix is isotropic. Secondly, radial, axial and circumferential stresses were investigated for each of the phases of two composite materials. The results of the studies showed that in case of uniaxial tension, the strength of the composite is controlled not by the strength of the fiber or the matrix, but is controlled by the strength of the viscous interphase layer.