The dissertation is concerned with concrete computations of modular spin characters of symmetric and alternating groups. We calculate all irreducible p-modular spin characters of the symmetric group Sym(n) and the alternating group Alt(n) for n=14,..,18 and p=3,5,7. Hence we obtain the p-modular decomposition numbers of projective representations of Sym(n) and Alt(n) for the specified values of n and p.