We present a novel incremental placement methodology called FlowPlace for significantly reducing critical path delays of placed standard-cell circuits. FlowPlace includes: a) a timing-driven (TD) analytical global placer TAN that uses accurate delay functions and minimizes a combination of linear and quadratic objective functions; b) a network flow based detailed placer TIF that has new and effective techniques for performing TD incremental placement and satisfying rowlength (white space) constraints. We have obtained results on three sets of benchmarks: i) TD versions of the ibm benchmark suite that we have constructed; ii) benchmarks used in TD-Dragon; iii) the Faraday benchmarks. Results show that starting with Dragon-placed circuits, we are able to obtain up to 34% and an average of 18% improvement in critical path delays, at an average of 17.5% of the run-time of the Dragon placer. Starting with a state-of-the-art TD placer TD-Dragon, for the TD-Dragon benchmarks we obtain up ...