Multimodal Transformers achieve superior performance in multimodal learning tasks. However, the quadratic complexity of the self-attention mechanism in Transformers limits their deployment in low-resource devices and makes their inference and training computationally expensive. We propose multimodal Sparse Phased Transformer (SPT) to alleviate the problem of self-attention complexity and memory footprint. SPT uses a sampling function to generate a sparse attention matrix and compress a long sequence to a shorter sequence of hidden states. SPT concurrently captures interactions between the hidden states of different modalities at every layer. To further improve the efficiency of our method, we use Layer-wise parameter sharing and Factorized Co-Attention that share parameters between Cross Attention Blocks, with minimal impact on task performance. We evaluate our model with three sentiment analysis datasets and achieve comparable or superior performance compared with the existing methods, with a 90% reduction in the number of parameters. We conclude that (SPT) along with parameter sharing can capture multimodal interactions with reduced model size and improved sample efficiency.