The architecture of Vision Transformers (ViTs), particularly the Multi-head Attention (MHA) mechanism, imposes substantial hardware demands. Deploying ViTs on devices with varying constraints, such as mobile phones, requires multiple models of different sizes. However, this approach has limitations, such as training and storing each required model separately. This paper introduces HydraViT, a novel approach that addresses these limitations by stacking attention heads to achieve a scalable ViT. By repeatedly changing the size of the embedded dimensions throughout each layer and their corresponding number of attention heads in MHA during training, HydraViT induces multiple subnetworks.