The paper deals with the excitation of the he[ium singlet level 2~P in the homogeneous and filamentary models of quiescent prominences with following parameters: the optical thickness at the limit of helium Lyman continuum ~,. = 0.1-100, T~ = 7000 K, n,. = 5 x 10~~ cm -3. Assuming a model He I atom with seven discrete levels (1 ~S, 2:~S, 2IS, 2~P, 2JP, 33D, 3JD) and the continuum the steady state equations for the levels 2:~S, 2~P and the continuum have been solved together with the radiative transfer equations for the line ).584 A and the continuum 2 < 504 A. The variations with depth of the functions n23s/n~s(z~,.), n2~p/n ~ ~s(Zj,,), and n~n,,/ni~s(zl,:) as well as the intensities of the triplet (D~, 210830 A) and singlet (~2 6678, 20 581 ~,) lines have been calculated. Comparison with observations leads to the following conclusions: (1) The line intensities calculated for filamentary models of prominences agree better with observations than those for homogeneous ones. (2)The helium level 2~P is excited by diffuse field 2584 )~ being formed by recombinations and spontaneous transitions 2JP -1 ~S and escaping from the promincnce into the space between the filaments and to the surface. (3) Underpopulation of the singlet level 2~P may be explained by combination of weak excitation mechanism (recombinations and formation of the diffuse field ).584 A) and strong decxcitation mechanism (spontaneous transitions into the level 1 ~S).