We present ab initio computations of the ionization of two-electron atoms by short pulses of intense linearly polarized Ti:sapphire laser radiation beyond the one-dimensional approximation. In the model the electron correlation is included in its full dimensionality, while the center-of-mass motion is restricted along the polarization axis. Our results exhibit a rich double ionization quantum dynamics in the direction transversal to the field polarization, which is neglected in the previous models based on the one-dimensional approximation.