Micro heat pipes are small structures that will be used to cool microscale devices. They function much like their conventional counterparts, with a few exceptions, most notably the absence of a wick. It is expected that water-filled micro heat pipes will be able to dissipate heat fluxes on the order of 10–15 W/cm2 (100,000–150,000 W/m2). This work addresses the modeling of a micro heat pipe operating under steady-state conditions. A one-dimensional model of the evaporator and adiabatic sections is developed and solved numerically to yield pressure, velocity, and film thickness information along the length of the pipe. Interfacial and vapor shear stress terms have been included in the model. Convection and body force terms have also been included in the momentum equation, although numerical experiments have shown them to be negligible. Pressure, velocity, and film thickness results are presented along with the maximum heat load dependence on pipe length and width. Both simple scaling and the model results show that the maximum heat transport capability of a micro heat pipe varies with the inverse of its length and the cube of its hydraulic diameter, implying the largest, shortest pipes possible should be used.