CaAFe4As4withA= K, Rb, and Cs are close to the doped 122 system, and the parent material can reach a superconducting transition temperature of 31–36 K without doping. To study the role of alkali metals, we investigated the induced hole doping and chemical pressure effects as a result of the introduction of alkali metals using density-functional-based methods. These two effects can affect the superconducting transition temperature by changing the number of electrons and the structure of the FeAs conductive layer, respectively. Our study shows that thedxzanddyzorbitals, which are degenerate in CaFe2As2, become nondegenerate in CaAFe4As4due to two nonequivalent arsenic atoms (As1 and As2). The unusual oblate ellipsoid hole pocket atΓpoint in CaAFe4As4results from a divalent cation Ca2+ replaced by a monovalent cationA+. It shows one of the main differences in fermiology compared to a particular form of CaFe2As2with reduced 1144 symmetry, due to the enhancement of As2-Fe hybridization. The unusual band appears in CaFe2As2(1144) and gradually disappears in the change of K to Cs. Further analysis shows that this band is contributed by As1 and has strong dispersion perpendicular to the FeAs layer, suggesting that it is related to the peculiar van Hove singularity below the Fermi level. In addition, various aspects of CaFe2As2(1144) and CaAFe4As4in the ground state are discussed in terms of the influence of hole doping and chemical pressure.