The low–lying electronic states (doublet and quartet) of the diatomic molecules BeK, BeRb and BeCs have been investigated theoretically based on the ab initio Complete Active Space Self Consistent Field (CASSF), and the Multi-Reference Configuration Interaction with Davidson correction MRCI+Q. The potential energy (PECs) and dipole moment (DMs) curves have been investigated for the 25, 28, and 24 low-lying electronic states in the representation of 2s+ (+/-) for BeK, BeRb, and BeCs molecules respectively along with the transition dipole moments (TDMs) between the ground state and four excited electronic states, in addition to static dipole polarizability for ground states. The spectroscopic constants, the internuclear distance Re, the rotational constant Be, and the electronic energy Te have been calculated. The vibrational energy Ev, the rotational constant Bv, the centrifugal distortion Dv, and the turning points Rmin and Rmax (up to vibrational level v =50) were obtained using the canonical function approach. By comparing our data with those given in literature (for several electronic states) shows a good agreement. This work represents investigation of new electronic states for BeX molecules (X=K, Rb and Cs) for the first time