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We present a self-consistent vertical disc model of thin and thick disc in the solar vicinity. The model is optimized to fit the local kinematics of main sequence stars by varying the star formation history and the dynamical heating function. The star formation history and the dynamical heating function are not uniquely determined by the local kinematics alone. For four different pairs of input functions we calculate star count predictions at high galactic latitude as a function of colour. The comparison with North Galactic Pole data of SDSS/SEGUE leads to significant constraints of the local star formation history

A detailed self-consistent vertical Milky Way disc model