The lasing dynamics of a stadium-cavity laser is studied by using a mode expansion model which is a reduction of the Schrödinger-Bloch model. We study the properties of stationary lasing states when two cavity modes are selectively excited, while examining the validity of the mode expansion model by comparing its results with those of the Schrödinger-Bloch model. Some analytical results are obtained for single-mode and two-mode stationary lasing states for the mode expansion model.