We report about the parallelisation of the algorithm to compute the normalised unit group V (FpG) of a modular group algebra FpG of a finite p-group G over the field of p elements Fp in the computational algebra system GAP. We present its distributed memory implementation using the new remote procedure call framework based on the the Symbolic Computation Software Composability Protocol (SCSCP). Using it, we were able for for the first time to perform practical computations of V (FpG) for groups of orders 29 and 36.