Numerical modelling is a tool to investigate the controls on the formation of the stratigraphic record on geological timescales. The model presented in this paper (DELTASIM) uses a process-response approach that simulates the stratigraphy of fluvial-dominated deltaic systems in two dimensions, based on simplified diffusion rules of cross-shore sedimentation. Net sedimentation is calculated for individual grain-size classes as the sum of independent erosion and deposition functions, enabling simulations of fluvio-deltaic stratigraphy besides clinoform evolution. Critical sediment transport parameters are validated using synthetic data from a process-based morphodynamic model, DELFT3D.Generic experiments show the effect of changes in sea level, sediment supply, offshore gradient and sediment size distribution. These experiments show that the model is fully capable of reproducing classic concepts of delta development on geological timescale. Such experiments allow students a possibility to evaluate the controls on the formation of the stratigraphic record. DELTASIM has been successfully applied to improve the understanding of the sedimentary evolution of a real-world fluvial-dominated delta in the Caspian Sea.Additional functionality encompasses a stochastic discharge model that can be used as input to simulate series of scenarios of delta development using the model's rapid run time to our advantage. This functionality enables us to present probabilistic output of longitudinal stratigraphic sections as an alternative to the deterministic predictions often made by stratigraphic models. The characteristics of the model; simplicity, speed and compatibility of the output to conceptual sequence stratigraphic models make DELTASIM suitable as a teaching tool.