Very high resolution (R similar to 200,000) and high signal-to-noise echelle spectra were obtained of comet Hyakutake (C/1996 B2) using the 2D coude: spectrograph on the 2.7 m telescope at W. J. McDonald Observatory during 1996 in late March and early April. Doppler resolved profiles are presented for individual lines of the major optical neutral species: CN, C-2, NH2, O(D-1) at 6300 Angstrom, and H Balmer-alpha at 6563 Angstrom. They are consistent with the expected expansion of a water-dominated cometary coma. Because of the small aperture and the small geocentric distance of the comet, the profiles of CN, C-2, and NH2 are totally shaped by the outflowing hydrodynamic coma. The NH, is the narrowest of the group because of the very short lifetime of the NH2 parent (NH3). The profile of C-2 is somewhat broadened, compared with NH2, because of the relatively larger contribution of C-2 radicals farther from the nucleus where the bulk outflow speed is larger. Any exothermic ejection speed they receive upon their production would be quenched. Although the profile of CN is broader than C-2, this is due to the fact that most of the CN lines are blends of two closely spaced but nearly equal strength components. Because O(1D) atoms in the region samples are produced mainly by the photodissociation of water which results in a prompt emission photon, the line retains contributions of both the basic coma expansion velocity and the 1.6 km s(-1) exothermal ejection speed of the O(D-1) atoms. The H Balmer-alpha line is complicated by a chance coincidence of a line of H2O+ and/or NH2 and by optical depth effects in solar Ly beta which are primarily responsible for the Balmer-alpha excitation. However, the width of the line wings is consistent with other comet observations, including Hyakutake itself, and the production by dissociation of H2O and OH and partial thermalization. We have successfully reproduced these data using a hybrid kinetic/hydrodynamic and Monte Carlo approach which include the important physical/chemical processes which can shape the spectral lines. Because the model includes no adjustable fitting parameters, the model-data agreement indicates that the underlying assumptions and calculated coma outflow speeds are quite reasonable.