When we build a neural network model predicting the relationship between two sentences, the most general and intuitive approach is to use a Siamese architecture, where the sentence vectors obtained from a shared encoder is given as input to a classifier. For the classifier to work effectively, it is important to extract appropriate features from the two vectors and feed them as input. There exist several previous works that suggest heuristic-based function for matching sentence vectors, however it cannot be said that the heuristics tailored for a specific task generalize to other tasks. In this work, we propose a new matching function, ElBiS, that learns to model element-wise interaction between two vectors. From experiments, we empirically demonstrate that the proposed ElBiS matching function outperforms the concatenation-based or heuristic-based matching functions on natural language inference and paraphrase identification, while maintaining the fused representation compact.