We investigate the initial stage of chromospheric evaporation in flares using soft X-ray spectra obtained by the Bragg Crystal Spectrometer (BCS) experiment on Yohkoh. We find that the centroid wavelength of the Ca XIX line in spectra with the first detectable emission is within about 8.5 × 10-4 A of the rest wavelength, which corresponds to a Doppler shift of no more than 80 km s-1. We also determine the minimum detectable soft X-ray flare volume emission measure from BCS Ca XIX flare spectra. We find that the minimum detectable emission measured by BCS is produced by an X-ray flux that is about equal to the peak intensity of a class A6 flare. These results are difficult to reconcile with one-dimensional hydrodynamic simulations of an impulsively heated flare loop, which predict large Doppler shifts during the initial stage of the heating. Furthermore, inspection of high spatial resolution TRACE images of flare plasma indicate significant differences between the observed morphology and the predictions of hydrodynamic models. The evolution of the intensity and the Doppler shifts are more consistent with models that assume the sequential heating of small-scale threads rather than the heating of an individual loop. However, the bright knots of emission and asymmetrical intensity distributions seen in flare images cannot be explained by current numerical models of chromospheric evaporation.