This paper studies the performance of multi-agent systems (MAS), the usage area of which is constantly expanding, under the fading effect of wireless communication channels. The main principle of multi-agent systems lies in solving difficult problems of high complexity and cost to single agents by employing many agents that can function without a central control unit. The consensus problem, which is used in order to achieve a common decision making by utilizing communication between agents, has been studied since long ago. However, even though MAS function through wireless communication channels, the effect of fading channel models on the consensus problem, have not been yet investigated in detail. This study analyzes this effect on the linear average consensus protocol. Monte Carlo simulations have been done on fixed topologies with different agent numbers and fading channel models for increasing SNR values.