We have carried out a study of the chemical abundances of $^1$H, $^4$He, $^{12}$C, $^{13}$C, $^{14}$N, $^{15}$N, $^{16}$O, $^{17}$O, $^{20}$Ne and $^{22}$Ne in symbiotic stars (SSs) by means of a population synthesis code. We find that the ratios of the number of O-rich SSs to that of C-rich SSs in our simulations are between 3.4 and 24.1, depending on the third dredge-up efficiency $��$ and the terminal velocity of the stellar wind $v(\infty)$. The fraction of SSs with $extrinsic$ C-rich cool giants in C-rich cool giants ranges from 2.1% to 22.7%, depending on $��$, the common envelope algorithm and the mass-loss rate. Compared with the observations, the distributions of the relative abundances of $^{12}$C/$^{13}$C vs. [C/H] of the cool giants in SSs suggest that the thermohaline mixing in low-mass stars may exist. The distributions of the relative abundances of C/N vs. O/N, Ne/O vs. N/O and He/H vs. N/O in the symbiotic nebulae indicate that it is quite common that the nebular chemical abundances in SSs are modified by the ejected materials from the hot components. Helium overabundance in some symbiotic nebulae may be relevant to a helium layer on the surfaces of white dwarf accretors.

28 pages, 6 figure, accepted for publication in ApJ