The earth is a natural, dynamic and evolving system which includes the atmosphere, hydrosphere, lithosphere and biosphere. Some fundamental internal and external processes are the consequences of the dynamic nature of the earth; namely, tectonic activity and earthquakes (geodynamic process); weathering, mass wasting and erosion (surface process); movement of water above, on and below the surface of the earth (hydrological process). All these processes have an active interaction and are also influenced by anthropogenic activities. CSIR-NGRI is actively involved in simulating the models for various earth processes through mathematical modelling, mainly Earthquake occurrence process models, Geodynamic models, Surface process model and Hydrological models. Understanding the earthquake occurrence processes and associated tectonic and anthropogenic deformation helps in taking up hazard mitigating measures. Geodynamic modelling helps us understand how long-term stress is distributed in various tectonic settings, which is also useful for understanding earthquake processes. Modelling of surface processes can help us understand the movement of earth’s materials and mitigate potential natural hazards like landslides. Hydrological processes modelling is crucial for developing sustainable water management strategies as well as modelling of floods and droughts in the face of changing climate. We are also involved in earthquake-triggered Tsunami modelling to forecast the time of its arrival, wave heights, and inundation extent in the vulnerable coastal plains, which can be used in coastal hazard mitigation.