Aiming at detecting pronunciation errors produced by second language learners and providing corrective feedbacks related with articulation, we address effective articulatory models based on deep neural network (DNN). Articulatory attributes are defined for manner and place of articulation. In order to efficiently train these models of non-native speech without such data, which is difficult to collect in a large scale, several transfer learning based modeling methods are explored. We first investigate three closely-related secondary tasks which aim at effective learning of DNN articulatory models. We also propose to exploit large speech corpora of native and target language to model inter-language phenomena. This kind of transfer learning can provide a better feature representation of non-native speech. Related task transfer and language transfer learning are further combined on the network level. Compared with the conventional DNN which is used as the baseline, all proposed methods improved the performance. In the native attribute recognition task, the network-level combination method reduced the recognition error rate by more than 10% relative for all articulatory attributes. The method was also applied to pronunciation error detection in Mandarin Chinese pronunciation learning by Japanese native speakers, and achieved the relative improvement up to 17.0% for detection accuracy and up to 19.9% for F-score, which is also better than the lattice-based combination.