The intriguing coexistence of the charge density wave (CDW) and superconductivity in SrPt2As2 and LaPt2Si2 has been investigated based on the ab initio density functional theory band structure and phonon calculations. We have found that the CDW instabilities for both cases arise from the q-dependent electron-phonon coupling with quasi-nesting feature of the Fermi surface. The band structure obtained by the band-unfolding technique reveals the sizable q-dependent electron-phonon coupling responsible for the CDW instability. The local split distortions of Pt atoms in the [As-Pt-As] layers play an essential role in driving the five-fold supercell CDW instability as well as the phonon softening instability in SrPt2As2. By contrast, the CDW and phonon softening instabilities in LaPt2Si2 occur without split distortions of Pt atoms. The phonon calculations suggest that the CDW and the superconductivity coexist in [X-Pt-X] layers (X = As or Si) for both cases.