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The structural stabilities, elastic properties and charge transfers of EuX (X = O, S, Se, Te) compounds as a function of pressure are investigated extensively using first-principles calculations. The ground-state parameters, such as lattice constants, bulk modulus are predicted and compared with the available data, our results are satisfactory. The calculated phase transition pressures from the NaCl-type (B1) structure to the CsCl-type (B2) structure for EuX (X = O, S, Se, Te) also accord with the experiments. Particularly, the elastic constants of EuX (X = O, S, Se, Te) under zero pressure and high pressure are simulated appropriately for the first time via density functional theory. The softening behaviors of the elastic shear modulus C44 under pressure for the B1 phase of EuX (X = O, S, Se, Te) are captured, which should be responsible for the pressure-induced structural phase transition in the EuX system. It is also suggested that the softening behavior might be induced partly by the p → d and f → d electron transfers of Eu atom under pressure. In addition, the aggregate elastic modulus (B, G, E), Poisson's ratio (σ), Debye temperature ϴD are also successfully obtained for both B1 and B2 phases of EuX. [ABSTRACT FROM AUTHOR]