Experiments were performed to measure the incipient boiling heat flux in a heat sink containing 21 rectangular (231 mum wide and 713 mum deep) micro-channels. Tests were performed using deionized water with inlet liquid velocities of 0.13-1.44 m/s, inlet temperatures of 30, 60 and 90 degreesC. and an outlet pressure of 1.2 bar, Using a microscope, boiling incipience was identified when the first bubbles were detected growing at, and departing from the micro-channel wall near the outlet. A comprehensive model was developed to predict the incipient boiling heat flux, accounting for the complexities of bubble formation along the flat and corner regions of a rectangular flow channel, as well as the likelihood of bubbles growing sufficiently large to engulf the entire flow area of a micro-channel. The model is based on a bubble departure criterion, which combines both mechanical considerations (force balance on a bubble) and thermal considerations (superheating entire bubble interface). The model shows good agreement with the experimental results.