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This paper deals with measuring the influence of observations on the results obtained with CART classification trees. To define the influence of individuals on the analysis, we use influence measures to propose criterions to quantify the sensitivity of the CART classification tree analysis. The proposals are based on predictions and use jackknife trees. The analysis is extended to the pruned sequences of CART trees to produce CART specific notions of influence. Using the framework of influence functions, distributional results are derived. A numerical example, the well known spam dataset, is presented to illustrate the notions developed throughout the paper. A real dataset relating the administrative classification of cities surrounding Paris, France, to the characteristics of their tax revenues distribution, is finally analyzed using the new influence-based tools. [ABSTRACT FROM AUTHOR]