The nu(3) and nu(4) vibrational transitions of methane trapped in solid parahydrogen have been observed by using Fourier transform infrared and high resolution laser spectroscopy. The observed spectrum is interpreted in terms of rovibrational states of the spherical rotor which are subjected to the crystal field splitting. The nu(4) band shows extremely sharp lines of a width of similar to 0.003 cm(-1), while the nu(3) band exhibits broader lines of a width of 1 cm(-1). The infrared selection rules derived from an extended group theory to take into account the field effect are consistent with the observed spectra. The intermolecular interaction and the field effect in solid parahydrogen are analyzed quantitatively. (C) 1997 American Institute of Physics.