Electronic band structure, optical and thermodynamic properties of ternary hydrides MBeH3 (M = Li, Na, and K) were studied using ab initio density functional theory (DFT). The effect of the adopted approximation to the exchange-correlation functional of the DFT is explicitly investigated by considering four different expressions of two different classes (local-density approximation and generalized-gradient approximation). The calculated magnitude of B classifies MBeH3 (M = Li, Na, and K) as easily compressible materials. The bonding interaction in these compounds is quite complicated. The interaction between M and BeH6 is ionic and that between Be and H comprises both ionic and covalent characters. The electronic structure of the complex hydride was investigated by calculating the partial and total densities of states, and electron charge density distribution. Large gaps in the density of states appear at the Fermi energy of LiBeH3, NaBeH3, and KBeH3 indicating that these classes of hydrides are insulators. Optical properties, including the dielectric function, reflectivity, and absorption coefficient, each as a function of photon energy, are calculated and show an optical anisotropy for LiBeH3 and KBeH3. Through the quasi-harmonic Debye model, in which the phononic effects are considered, temperature dependence of volume V(T), bulk modulus B(T), and thermal expansion coefficient alpha(T), constant-volume and constant-pressure specific heat (C-v and C-p) and Debye temperature Theta(D), the entropy S, and the Gruneisen parameter gamma were calculated at wide pressure and temperature ranges. The principal aspect of the obtained results is the close similarity of MBeH3 (M = Li, Na, and K) compounds.