The infrared absorption spectrum of solid SiH4 has been measured between 4000 and 10500 cm(-1) in both phases I and II. Eighteen new overtone and combination bands have been observed and assigned. Some of them correspond to sets of propagating vibrons, others to localized overtones with strong anharmonicities. The observations of the overtones (n-1)nu(1)+nu(3) (n=2,3,4,5) are in excellent agreement with a local mode approach, usually applied to the vibrations of isolated molecules. Its use provides a determination of both the harmonic and anharmonic parameters of the SiH4 stretching in the solid phase. (C) 1997 American Institute of Physics. [S0021-9606(97)01041-6].