In this paper, we propose a via distribution model for yield estimation. This model expresses a relationship between the number of vias and wire length. We also provide an estimate for the total number of vias in a circuit, derived from the via distribution and the wire-length distribution. The via distribution is modeled as a function of track utilization, and the wire-length distribution can be derived from the gate-level netlist and the layout area. We extract model parameters from the commercial chips designed for 0.18-µm and 0.13-µm CMOS processes, and demonstrate the yield degradation caused by vias.