The circadian locomotor output cycles kaput (CLOCK), and brain and muscle ARNT-like 1 (BMAL1) proteins are important transcriptional factors of the endogenous circadian clock. The CLOCK and BMAL1 proteins can regulate the transcription-translation activities of the clock-related genes through the DNA binding. The hetero-/homo-dimerization and DNA combination of the CLOCK and BMAL1 proteins play a key role in the positive and negative transcriptional feedback processes. In the present work, we constructed a series of binary and ternary models for the bHLH/bHLH-PAS domains of the CLOCK and BMAL1 proteins, and the DNA molecule, and carried out molecular dynamics simulations, free energy calculations and conformational analysis to explore the interaction properties of the CLOCK and BMAL1 proteins with DNA. The results show that the bHLH domains of CLOCK and BMAL1 can favorably form the heterodimer of the bHLH domains of CLOCK and BMAL1 and the homodimer of the bHLH domains of BMAL1. And both dimers could respectively bind to DNA at its H1-H1 interface. The DNA bindings of the H1 helices in the hetero- and homo-bHLH dimers present the rectangular and diagonal binding modes, respectively. Due to the function of the α-helical forceps in these dimers, the tight gripping of the H1 helices to the major groove of DNA would cause the decrease of interactions at the H1-H2 interfaces in the CLOCK and BMAL1 proteins. The additional PAS domains in the CLOCK and BMAL1 proteins affect insignificantly the interactions of the CLOCK and BMAL1 proteins with the DNA molecule due to the flexible and long loop linkers located at the middle of the PAS and bHLH domains. The present work theoretically explains the interaction mechanisms of the bHLH domains of the CLOCK and BMAL1 proteins with DNA.