3 stable and 6 stable structure of electronic states for La_(3) and La_(4) are found using the density functional method B3LYP with relativistic effective core potentials, respectively. The most stable electronic state is of D_(3h )structure for La_(3) and the planar C_(2v )structure for La_(4).The analysis of the relationships among these various geometrical configurations, based on the Jahn-Teller effect, vibronic interaction and the resolution of group representations, is in agreement with the calculated results.