This paper studies the behavior of a platoon control system under the presence of inter-vehicle noisy communication channels. A set of homogeneous vehicles modelled as LTI systems with a predecessor-following topology is analyzed. Our main contribution is to study the stochastic scenario when additive white noise is affecting the communication between agents. We aim to provide conditions for mean square string stability and look over its relationship with the mean and variance of the tracking error. Finally, through computational analysis, we discuss the scalability, convergence and boundedness properties related to string stability in stochastic multi-agent systems. Copyright (C) 2020 The Authors.