Various theories have been proposed in the field of second language (L2) sentence processing research and have significantly advanced our understanding of the mechanisms underlying L2 sentence interpretation processes. However, many existing theories have only been formulated verbally, and little progress has been made towards formal modelling. Formal modelling offers several advantages, including enhancing the clarity and verifiability of theoretical claims. This paper aims to address this gap in the literature by introducing formal computational modelling and demonstrating its application in L2 sentence processing research. Through practical demonstrations, the paper also emphasises the importance of formal modelling in the formulation and development of theory.