CS30301--015 and HE1045+0226 are two metal-poor stars which show overabundance of both C and s-process elements (i.e., CEMP-s stars). The radial velocity observations suggest that these two CEMP-s stars have constant radial velocities and suggested that CS30301--015 and HE1045+0226 could be single stars. Study of the astrophysical origins of chemical elements in the two apparently-single CEMP-s stars can provide useful clues for better understanding the chemical evolution of the early Galaxy. Based on the superposition and decomposition calculations, we investigated the astrophysical origins of chemical elements in the two sample stars. We found that the lighter and Fe-group elements of these two sample stars are mainly produced by primary process in massive stars. For CS30301--015, the neutron-capture elements dominantly originate from the main s-process in Asymptotic Giant Branch (AGB) stars. The high Pb abundance can be explained by the contribution of main s-process. The contributed fraction of main s-process to Pb is about 99.8%. More radial-velocity observations are needed to confirm the orbital features of this sample star. While for the other sample star HE1045+0226, the heavier neutron-capture elements with≤56Z≤62 are mainly produced by main s-process and Eu mainly originate from main r-process, Z is the proton number. However, the lighter neutron-capture elements Y and Zr mainly come from the primary weak s-process occurring in fast rotation massive stars. The contributed fractions of the primary weak s-process to Y and Zr abundances of HE1045+0226 are about 69.8% and 67.6%, respectively. This suggests that the apparently-single CEMP-s star HE1045+0226 should have the footprints of primary weak s-process. The conclusions prove that weak s-process could occur in metal-poor environments.