This paper proposes the adaptation of Support Vector Data Description (SVDD) to the multiple kernel case (MK-SVDD), based on SimpleMKL. It also introduces a variant called Slim-MK-SVDD that is able to produce a tighter frontier around the data. For the sake of comparison , the equivalent methods are also developed for One-Class SVM, known to be very similar to SVDD for certain shapes of kernels. Those algorithms are illustrated in the context of 3D-shapes filtering and outliers detection. For the 3D-shapes problem, the objective is to be able to select a sub-category of 3D-shapes, each sub-category being learned with our algorithm in order to create a filter. For outliers detection, we apply the proposed algorithms for unsupervised outliers detection as well as for the supervised case.