This paper studies the physical layer security of a vehicular communication network in the presence of interference constraints by analysing its secrecy capacity. The system considers a legitimate receiver node and an eavesdropper node, within a shared network, both under the effect of interference from other users. The double-Rayleigh fading channel is used to capture the effects of the wireless communication channel for the vehicular network. We present the standard logarithmic expression for the system capacity in an alternate form, to facilitate analysis in terms of the joint moment generating functions (MGF) of the random variables representing the channel fading and interference. Closed-form expressions for the MGFs are obtained and Monte-Carlo simulations are provided throughout to validate the results. The results show that performance of the system in terms of the secrecy capacity is affected by the number of interferers and their distances. The results further demonstrate the effect of the uncertainty in eavesdropper location on the analysis.