[en] The Weakest Bound Electron Potential Model (WBEPM) is used to calculate transition probabilities between LS multiplets of Be I, Be II, Mg I, and Mg II. In this calculation, a coupled set of equations is employed to determine effective charges Z* and effective quantum numbers n* and l* using, as input data, experimental energy levels and radial expectation values obtained with the numerical Coulomb approximation. Transition probabilities between highly excited states are evaluated using modified hydrogenic wavefunctions. Good agreement is seen in comparisons of the present results with those from other works