A major issue in the activity of deductive program verification is to understand why automated provers fail to discharge a proof obligation. To help the user understand the problem and decide what needs to be fixed in the code or the specification, it is essential to provide means to investigate such a failure. We present our approach for the design and the implementation of counterexample generation, exhibiting values for the variables of the program where a given part of the specification fails to be validated. To produce a counterexample, we exploit the ability of SMT solvers to propose, when a proof of a formula is not found, a counter-model. Turning such a counter-model into a counterexample for the initial program is not trivial because of the many transformations leading from a particular piece of code and its specification to a set of proof goals given to external provers.