Wav2vec 2.0 is a recently proposed self-supervised framework for speech representation learning. It follows a two-stage training process of pre-training and fine-tuning, and performs well in speech recognition tasks especially ultra-low resource cases. In this work, we attempt to extend the self-supervised framework to speaker verification and language identification. First, we use some preliminary experiments to indicate that wav2vec 2.0 can capture the information about the speaker and language. Then we demonstrate the effectiveness of wav2vec 2.0 on the two tasks respectively. For speaker verification, we obtain a competitive result with the Equal Error Rate (EER) of 3.61% on the VoxCeleb1 dataset. For language identification, we obtain an EER of 12.02% on the 1 second condition and an EER of 3.47% on the full-length condition of the AP17-OLR dataset. Finally, we utilize one model to achieve the unified modeling by the multi-task learning for the two tasks.