This article is concerned with variable selection for cluster analysis. The problem is regarded as a model selection problem in the model-based cluster analysis context. A general model generalizing the model of Raftery and Dean (2006) is proposed to specify the role of each variable. This model does not need any prior assumptions about the link between the selected and discarded variables. Models are compared with BIC. Variables role is obtained through an algorithm embedding two backward stepwise variable selection algorithms for clustering and linear regression. The consistency of the resulting criterion is proved under regularity conditions. Numerical experiments on simulated datasets and a genomics application highlight the interest of the proposed variable selection procedure.