Vehicular ad hoc networks (VANETs) have recently attracted interest for automation and intelligent transportation system (ITS). In this paper, to assess the performance of the IEEE 802.11p medium access control (MAC) for VANETs, an analytical model based on Markov chain model is presented. The parameters that could impact performance such as number of vehicles, velocity, vehicle density, contention window (CW) size, packet size, transmission range etc. are taken into consideration. The relationship among parameters and performance metrics are derived. The probability of successful transmission, throughput, and delay expressions are obtained. Furthermore, to verify the analytical studies numerical results are presented and whether the IEEE 802.11p can fulfill the performance criteria for VANETs or not is checked.