We aim at exploring the potential of parallel computations in the offline phase of the Reduced Basis Method (RBM) to obtain some speed-up in particular in those cases where the snapshot computation is extremely costly. In order to do so, we introduce a batch size b and add the snapshots with the b largest (estimated) error values to the current basis. These snapshots are computed in parallel. We prove convergence rates for this new batch greedy algorithm for polynomial and exponential decay of the Kolmogorov width and present numerical results where we apply a (parallel) implementation of the proposed algorithm to a linear elliptic and a nonlinear elliptic problem.