A model for the elastic coefficients of fiber-reinforced materials is applied toward the analysis of the tensile and shear moduli of nanocomposites reinforced by rod-like cellulose nanoparticles. Our formalism integrates results from percolation theory with micromechanical and effective medium approaches Polydispersity in the fiber length distribution and anisotropics in the stiffness coefficients of cellulose nanoparticles are taken into account explicitly. Results from calculations employing our model display reasonable agreement with experimental measurements of the moduli as functions of the filler volume fraction for several cellulose nanoparticle-reinforced thermoplastic-based composites.