Based on the time dependent theory of random lasers, which was established via combining Maxwell equations with the rate equations of a four-level atomic system, the output intensity of lasing modes varying with the pump rate and area as well as the medium's size and shape is simulated for two-dimensional random media by use of the finite difference time domain method. Results show that the pump-rate dependence of the output intensity presents not only a threshold property, but also a saturation property, just like that of the lasing modes in conventional lasers. Based on the dependence of mode property on the medium's and pump's parameters, the mode-selection approaches are proposed for two-dimensional random lasers, which are quite different from those performed in conventional lasers.