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The anomalous oxygen isotope shift observed in the high-temperature superconductors La(2-x)Sr(x)CuO4 and La(2-x)Ba(x)CuO4 is discussed within the model of superconductivity in which the apex oxygen vibrations play the major role in the pairing mechanism. We show that the dependence of both the critical temperature and its isotope shifts on the doping level is consistently described within this model. The anomaly occurring in the isotope shift between x = 0.11 and x = 0.15 is traced back to the oxygen mass exponent associated with the apex oxygen frequency. (Author)