In this paper, we develop the queuing system model with processor sharing discipline with random serving rate coefficients. Each arriving customer is characterized by its length (job volume) and a serving rate coefficient determined by some probability distributions. The coefficients remain constant during the service process of customers. The proposed model is aimed to model the service process of elastic sessions in wireless networks, in which each session is assigned to one of modulation and coding schemes (MCSs) according to the state of the radio channel. Each MCS is characterized by its value of the spectral efficiency, which is modeled by serving rate coefficients. First, we analyze the proposed model. Then we apply a simplification that significantly reduces the complexity of the analysis and allows us to deduce formulas for the blocking probability and the average sojourn time. Finally, we conduct a numerical analysis of the considered model. © 2021, Springer Nature Switzerland AG.