In India, the most widely used means of transportation is motorised two-wheelers (MTWs), accounting for 70.5% of all registered vehicles and classified as the most vulnerable road users. The steady rise in this transportation category results in increased accidents and fatalities. Conventionally, traffic safety studies are focused on car-based or mixed-traffic data. The aim of the study is to model critical conflicts of MTWs at unsignalised intersections. A videographic survey was done to collect necessary traffic data and traffic flow characteristics from four unsignalised intersections in Assam, India. Based on the type of interactions, three subcategories were formed mainly—Two-Wheeler-Two-Wheeler (2W-2W), Two-Wheeler-Three-Wheeler (2W-3W), and Two-Wheeler-Four-Wheeler (2W-4W). The interaction is further divided into critical conflicts and non-critical conflicts by considering a threshold value of 1.5 s for PET values. Preliminary analysis showed that 2W-2W interaction contributed the most to the critical crossing conflicts. The critical conflicts were modelled using the Poisson-Tweedie regression technique. Based on the findings, the intersection geometry, traffic volume, and 2W-2W interaction have the greatest influence on the number of crossing conflicts. The model used in the study can be utilised to forecast critical traffic conflicts and improve safety at unsignalised intersections.