RePlAce is a state-of-the-art prototype of a flat, analytic, and nonlinear global cell placement algorithm, which models a placement instance as an electrostatic system with positively charged objects. It can handle large-scale standard-cell and mixed-cell placement, while achieving shorter wirelength and similar or shorter runtimes than other state-of-the-art placers on the ISPD-2005/2006 standard-cell benchmarks; however, the runtime of RePlAce on these benchmarks ranges from 15 minutes to 5+ hours on a 2.6 GHz Intel Xeon server running a single thread, rendering development cycles prohibitively long. To address this concern, this paper introduces a multi-threaded shared-memory implementation of RePlAce. The contributions include techniques to reduce memory contention and to effectively balance the workload among threads, targeting the most substantial performance bottlenecks. With 2–12 threads, our parallel RePlAce speeds up the bin density function by a factor of 4.2–10×, the wirelength function by a factor of 2.3–3×, and the cost gradient function by a factor of 2.9–6.6× compared to the single-threaded original RePlAce baseline. Moreover, our parallel RePlAce is ≈3.5× faster than the state-of-the-art PyTorch-based placer DREAMPlace, when both are running on 12 CPU cores.