Nanocomposites based on ethylene-co-vinyl acetate (EVA) and silica oxide (SiO₂), with nanometric size (40nm) were prepared by solution process, employing chloroform as solvent. The nanocomposites were mainly characterized by solid state nuclear magnetic resonance spectroscopy (NMR). From the methodology employed polymer matrix was evaluated by the determination of proton nuclear spin-lattice relaxation time (T₁H) and spin-spin relaxation time (T₂H) employing low field NMR spectrometer and also applying carbon-13 (¹³C) solid-state NMR techniques and proton spin-lattice relaxation time in the rotating frame (T_1pH) by high field NMR. The nanoparticle, silica oxide, was analyzed by silicon-29 (²⁹Si) NMR MAS spectrum. The evaluation of relaxation time showed an increase in the proton spin-lattice relaxation time, because of silicon nucleus interaction with polymer chains promoting an increase in the sample rigidity, which is a result of good silica oxide dispersion in the polymeric matrix. The nanomaterial with 5% of SiO₂presented good dispersion of silica oxide in the polymeric matrix, because of the formation of strong intermolecular interaction.