Three-dimensional morphable models of object classes are a powerful tool in modeling, animation and recognition. We introduce here the new concept of regularized 3D morphable models, along with an iterative learning algorithm, by adding in the statistical model a noise/regularization term which is estimated from the examples set. With regularized 3D morphable models we are able to handle missing information, as it often occurs with data obtained by 3D acquisition systems; additionally, the new models are less complex than, but as powerful as the non-regularized ones. We present the results obtained for a set of 3D face models and a comparison with the ones obtained by a traditional morphable model on the same data set.