We present a new type of flow model suitable for Antarctic blue ice areas, with application to dating ice for paleoclimate purposes. The volume conserving model uses field data for surface velocities, mass balance and ice thickness along a flow line, with parameterized variation of ice rheology with depth to produce particle trajectories and isochrones. The model is tested on the contrasting Allan Hills Near Western Ice Field and the Scharffenbergbotnen blue ice fields in Antarctica by comparing predicted ages with ages inferred from meteorites and 14C data. During the glacial periods, ice surface velocities at the Allan Hills must have been 25% less, and accumulation rates 50% less than present day values in order to match meteorite ages. In contrast, Scharffenbergbotnen velocities have probably been fairly constant over time due to the atypical valley where it resides.