This article describes an approximate model of a group of cells in the wireless 4G network with implemented load balancing mechanism. An appropriately modified model of Erlang's Ideal Grading is used to model this group of cells. The model makes it possible to take into account limited availability of resources of individual cells to multi-rate elastic and adaptive traffic streams generated by Erlang and Engset sources. The developed solution allows the basic traffic characteristics in the considered system to be determined, i.e. the occupancy distribution and the blocking probability. Because of the approximate nature of the proposed model, the results obtained based on the model were compared with the results of a digital simulation. The present study validates the adopted assumptions of the proposed model.