We have theoretically examined the sensitivity of the curve-of-growth (COG) technique utilized in rocket measurements to determine the line profiles of the solar He I resonance emissions. In the present work we are primarily interested in the possibility of determining the line core shape using this technique. We have selected the line at 584.334 ¿ as an illustration. Various possible source functions of the solar line have been assumed in the computation of the integrated transmitted intensity. A recent observational data set obtained by our group is used as the constraint of the computation. We have confirmed that the COG technique can indeed provide a good measurement of the solar line width. However, to obtain detailed knowledge of the solar profile at line center and in the core region, (1) it is necessary to be able to carry out relative solar flux measurements with a 1% or better precision, and (2) we must be able to measure the He gas pressure in the absorption cell to lower than 0.1 mtorr. While these numbers apply specifically to our own geometry, the results are readily scaled to othe COG measurements using other experimental parameters.