  In this work, we study the parallel-in-time iterative solution of coupled
flow and geomechanics in porous media, modelled by a two-field formulation of
the Biot's equations. In particular, we propose a new version of the fixed
stress splitting method, which has been widely used as solution method of these
problems. This new approach forgets about the sequential nature of the temporal
variable and considers the time direction as a further direction for
parallelization. We present a rigorous convergence analysis of the method and a
numerical experiment to demonstrate the robust behaviour of the algorithm.
