This paper presents a model that describes how liquid flow fills micro-fluidic components and networks. As an alternative to computational fluid dynamic (CFD) simulations, we use a constrained energy minimization approach. This approach is based on two assumptions that hold in many micro-fluidic devices: (i) The length scales are small, and we consider slow filling rates, hence fluid momentum and viscous terms are small compared to surface tension forces, consequently the liquid/gas interfaces can be viewed as a succession of quasi-steady equilibrium configurations. (ii) Any equilibrium configuration corresponds to a surface tension energy minima which is constrained by the device shape and the volume of liquid in the device. The model is developed for planar micro-fluidic devices, is based on a fundamental physical principle, and shows accurate agreement with experimental data. It takes us only a few minutes to evaluate the model for a planar component of any shape using the Surface Evolver software, and this is significantly less then the computer run time required for CFD simulations. Moreover, once a library of component models has been created (which takes less than an hour of computer time) it then takes only seconds to simulate different network architectures with thousands of components. This fast "reconfigure the network and simulate in seconds" capability is essential for the design of truly complex networks that will enable the next generation of passive, micro-fluidic, lab-on-a-chip systems.