  We present spectral fits to five epochs of the typical Type Ib supernova
1999dn using the generalized, non-LTE, stellar atmospheres code PHOENIX. Our
goal is threefold: to determine basic physical properties of the supernova
ejecta, such as velocity, temperature, and density gradients; to reproduce He I
absorption lines by invoking non-thermal excitation; and, to investigate
possible spectral signatures of hydrogen, especially a feature around 6200
Angstrom, which has been attributed to high velocity $H_\alpha$. Our models
assume an atmosphere with uniform composition devoid of any hydrogen. Our model
spectra fit the observed spectra well, successfully reproducing most of the
features, including the prominent He I absorptions. The most plausible
alternative to $H_\alpha$ as the source of the 6200 Angstrom feature is a blend
of Fe II and Si II lines, which can be made stronger to fit the observed
feature better by increasing the metallicity of the ejecta. High-metallicity
models fit well at early epochs, but not as well as solar-metallicity models
after maximum light. While this blend of metal lines is a reasonable
explanation of the source of the 6200 Angstrom feature, it is still important
to investigate hydrogen as the source; therefore, a second paper will present
models that include a thin shell of hydrogen around the main composition
structure.
