The ground-state structure, equilibrium structural parameters, electronic structure, and thermodynamical properties of MCaH(3) (M=Li, Na, K, Rb, and Cs) phases have been investigated. From the 104 structural models used as inputs for structural optimization calculations, the ground-state crystal structures of MCaH(3) phases have been predicted. At ambient condition, LiCaH(3), NaCaH(3), and KCaH(3) crystallize in hexagonal, monoclinic, and orthorhombic structures, respectively. The remaining phases RbCaH(3) and CsCaH(3) crystallize in a cubic structure. The calculated phonon spectra indicate that all the predicted phases are dynamically stable. The formation energy for the MCaH(3) phases have been calculated along different reaction pathways. The electronic structures reveal that all these phases are insulators with an estimated band gap varying between 2.5 and 3.3 eV.