We consider the modeling and experiments with polymer dye-doped lasers shaped as thin flat cavities, allowing one to consider them as two-dimensional (2-D) active cavities. We focus our modeling on the H-polarized electromagnetic field in a kite-shaped laser. Assuming that the lasing-mode frequency is real-valued, we look for it together with the corresponding threshold value of material gain. Such electromagnetic-field problem is reduced to the Muller set of the boundary integral equations (MBIE), discretization of which yields determinantal equation. Numerical results reveal various types of modes existing in the kite including the perturbed whispering gallery (WG) modes that have the lowest thresholds. Their far-field emission patterns show good agreement with the measurements. © 2015 IEEE.