Nanocomposite is modeled as a linearly elastic composite medium, which consists of a homogeneous matrix containing a statistically homogeneous random field of homogeneous prolate spheroidal nanofibers with prescribed random orientation. Estimation of effective elastic moduli of nanocomposites was performed by the version of effective field method (see for references Buryachenko VA. Multiparticle effective field and related methods in micromechanics of composite materials. Appl Mech Rev 2001;54:1-47) developed in the framework of quasi-crystalline approximation when the spatial correlations of inclusion location take particular ellipsoidal forms. The independent justified choice of shapes of inclusions and correlation holes provide the formulae of effective moduli which are symmetric, completely explicit and easily to use. The parametric numerical analyses revealed the most sensitive parameters influencing the effective moduli which are defined by the axial elastic moduli of nanofibers rather than their transversal moduli as well as by the justified choice of correlation holes, concentration and prescribed random orientation of nanofibers.