Abstract We present formal definitions of anonymity properties for voting protocols using the process algebra CSP. We analyse a number of anonymity definitions, and give formal definitions for strong and weak anonymity, highlighting the difference between these definitions. We show that the strong anonymity definition is too strong for practical purposes; the weak anonymity definition, however, turns out to be ideal for analysing voting systems. Two case studies are presented to demonstrate the usefulness of the formal definitions: a conventional voting system, and Prêt à Voter, a paper-based, voter-verifiable scheme. In each case, we give a CSP model of the system, and analyse it against our anonymity definitions by specification checks using the Failures-Divergences Refinement (FDR2) model checker. We give a detailed discussion on the results from the analysis, emphasizing the assumptions that we made in our model as well as the challenges in modelling electronic voting systems using CSP.