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The photodetachment cross section of H[?] in parallel electric and magnetic fields near an elastic surface is derived and calculated by using the closed orbit theory. It is found that the elastic surface can produce some interesting effects. Besides the closed orbits previously found by Peters et al. for the H[?] in parallel electric and magnetic fields, some additional closed orbits are produced due to the effect of the elastic surface. The results show that the cross section oscillation is much more complicated in comparison with the cross section of H[?] in parallel external fields without surface. Each peak in the Fourier transformed cross section corresponds to the period of one detached electron closed orbit. This study provides a new understanding of the photodetachment of negative ions in the presence of external fields and surface. [ABSTRACT FROM AUTHOR]