The performance of impingement air cooled plate fin heat sinks differs significantly from that of parallel flow plate fin heat sinks. A simple impingement flow pressure drop model based on developing laminar flow in rectangular channels is proposed. The model is developed from simple momentum balance and utilizes fundamental solutions from fluid dynamics to predict its constitutive components. To test the validity of the model, experimental measurements of pressure drop are performed with heat sinks of various impingement inlet widths, fin spacings, fin heights, and airflow velocities. The accuracy of the pressure drop model was found to be within 20% of the experimental data taken on four heat sinks and other experimental data from the published literature at channel Reynolds numbers less than 1200. The simple model is suitable for impingement air cooled plate fin heat sinks parametric design studies.