We present a series of simple shear numerical simulations of dynamic recrystallization of two‐phase non‐linear viscous materials that represent temperate ice. Firstly, we investigate the effect of the presence of water on the resulting microstructures and, secondly, how water influences on P‐wave (Vp) and fast S‐wave (Vs) velocities. Regardless the water percentage, all simulations evolve from a random fabric to a vertical single maximum. For a purely solid aggregate, the highest Vp quickly aligns with the maximum c‐axis orientation. At the same time, the maximum c‐axis development reduces Vs in this orientation. When water is present, the developed maximum c‐axis orientation is less intense, which results in lower Vp and Vs. At high percentage of water, Vp does not align with the maximum c‐axis orientation. If the bulk modulus of ice is assumed for the water phase (i.e., implying that water is at high pressure), we find a remarkable decrease of Vs while Vp remains close to the value for purely solid ice. These results suggest that the decrease in Vs observed at the base of the ice sheets could be explained by the presence of water at elevated pressure, which would reside in isolated pockets at grain triple junctions. Under these conditions water would not favor sliding between ice grains. However, if we consider that deformation dominates over recrystallization water pockets get continuously stretched, allowing water films to be located at grain boundaries. This configuration would modify and even overprint the maximum c‐axis‐dependent orientation and the magnitude of seismic anisotropy.