Rank data arise from a sorting mechanism which is generally unobservable for the statistician. Retaining the insertion sorting algorithm because of its well known optimality properties and combining it with a natural stochastic error in the pair comparison process allows to propose a parsimonious and meaningful parametric generative model for rank data. Its theoretical properties are studied like unimodality, symmetry and identifiability. In addition, maximum likelihood principle can be easily performed through an EM algorithm thanks to an unobserved latent variables interpretation of the model. Finally, an illustration of adequacy between the proposed model and rank data resulting from a general knowledge quiz suggests the relevance of our proposal.