A Boundary Integral Method (BIM) for simulation of foam formation and dynamics in viscous flows is presented. The main features of the numerical method are: Nonsingular contour integration of the singular single layer potential; Higher order approximation of the interface positions and the distance between the interfaces; Dynamic mesh regularization. Presented are also results of foam-drop formation and its dynamic behavior in a viscous flow. They demonstrate the ability of the presented numerical method for simulation of polydisperse foam dynamics as well as dynamics of drops at very close distance.