Self-supervised foundation models have shown great potential in computer vision thanks to the pre-training paradigm of masked autoencoding. Scale is a primary factor influencing the performance of these foundation models. However, these large foundation models often result in high computational cost that might limit their deployment. This paper focuses on pre-training relatively small vision transformer models that could be efficiently adapted to downstream tasks. Specifically, taking inspiration from knowledge distillation in model compression, we propose a new asymmetric masked distillation(AMD) framework for pre-training relatively small models with autoencoding. The core of AMD is to devise an asymmetric masking strategy, where the teacher model is enabled to see more context information with a lower masking ratio, while the student model still with high masking ratio to the original masked pre-training. We design customized multi-layer feature alignment between the teacher encoder and student encoder to regularize the pre-training of student MAE. To demonstrate the effectiveness and versatility of AMD, we apply it to both ImageMAE and VideoMAE for pre-training relatively small ViT models. AMD achieved 84.6% classification accuracy on IN1K using the ViT-B model. And AMD achieves 73.3% classification accuracy using the ViT-B model on the Something-in-Something V2 dataset, a 3.7% improvement over the original ViT-B model from VideoMAE. We also transfer AMD pre-trained models to downstream tasks and obtain consistent performance improvement over the standard pre-training.