A mathematical model is formulated and solved numerically describing the local thinning of liquid films between a solid/liquid interface and a fluid/liquid interface with a variable surface concentration of an insoluble surfactant. Reynolds lubrication approximation is used. The initial excess surfactant distribution is two-dimensional Gaussian. The film thins most rapidly at the center of the disturbance until a thickness is reached at which rupture may occur. Alternatively a minimum film thickness is reached after which the film recovers and eventually regains its original thickness. The time to reach the minimum thickness lengthens as the background concentration of surfactant approaches zero.