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Differential Evolution is a simple and efficient stochastic, population-based heuristics for global optimization over continuous spaces. As with other nature inspired techniques, there is no provision for constraint handling in its original formulation, and a few possibilities have been proposed in the literature. In this paper an adaptive penalty technique (APM), previously developed and applied to genetic algorithms, is considered for constraint handling within differential evolution. The technique requires no extra parameters. Based on feedback obtained from the current status of the population of candidate solutions, the technique automatically defines, for each constraint, its corresponding penalty coefficient. Equality as well as inequality constraints can be dealt with. The APM technique, which has been shown to be quite effective within genetic algorithms, is adapted here to the differential evolution context. In order to assess the applicability and performance of the proposed constraint handling scheme, several test-problems from the structural and mechanical engineering optimization literature are considered. 2. Keywords: Differential Evolution, Constrained Optimization, Adaptive Penalty.