A fully dynamic model of a microchannel evaporator is presented. The aim of the model is to study the highly dynamic parallel channel instabilities that occur in these evaporators in more detail. The numerical solver for the model is custom-built and the majority of the paper is focused on detailing the various aspects of this solver. The one-dimensional homogeneous two-phase flow conservation equations are solved to simulate the flow. The full three-dimensional (3D) conduction domain of the evaporator is also dynamically resolved. This allows for the correct simulation of the complex hydraulic and thermal interactions between the microchannels that give rise to the parallel channel instabilities. The model uses state-of-the-art correlations to calculate the frictional pressure losses and heat transfer in the microchannels. In addition, a model for inlet restrictions is also included to simulate the stabilizing effect of these components. In the final part of the paper, validation results of the model are presented, in which the stability results of the model are compared with the existing experimental data from the literature. Next, a parametric study is performed focusing on the stabilizing effects of the solid substrate properties. It is found that increasing the thermal conductivity and thickness of the solid substrate has a strong stabilizing effect, while increasing the number of microchannels has a small destabilizing effect. Finally, representative dynamic results are also given to demonstrate some of the unique capabilities of the model.