Making an accurate prediction of occupancy and flow is essential to enable better safety and interaction for autonomous vehicles under complex traffic scenarios. This work proposes STrajNet: a multi-modal Swin Transformerbased framework for effective scene occupancy and flow predictions. We employ Swin Transformer to encode the image and interaction-aware motion representations and propose a cross-attention module to inject motion awareness into grid cells across different time steps. Flow and occupancy predictions are then decoded through temporalsharing Pyramid decoders. The proposed method shows competitive prediction accuracy and other evaluation metrics in the Waymo Open Dataset benchmark.